Aria/WMG

Cait Sith is the all-powerful ruler of Aqua.
Cait Sith rules Aqua with an iron fist in a velvet glove. Crime, poverty, fear, hatred, and idiocy don't exist on Aqua because the immortal, heavily bioengineered, enormous-brained, trans-singularitan cat doesn't think they should. And all the weird events? It's not Akari daydreaming, they really happen because he has Sufficiently Advanced Technology, local control of spacetime, and he wants them to.

Alicia's marriage was an arranged one.
First, we never get to see the lucky hubbie, nor is he mentioned at any time what-so-ever. So, an arranged marriage is a pretty good explanation for why Alicia just jumped into a marriage without ever seeing the guy in at least 4 years. Secondly, there is the timing. I mean, getting hitched as soon as Akari becomes capable of taking over? It's likely that the families were pressuring her and Alicia probably promised to marry as soon as she could find a suitable person to take over Aria Company. Third, there is numerous examples of Values Dissonance such as females retiring when they marry, so arranged marriage isn't too crazy of an idea.
 * In the manga there are some hints Alicia is seeing someone, even though she never even introduces the guy (?) to anyone.
 * It's said several times that the reason she is retiring as an undine is not her marriage, it's the shift in job to working at the Gondola Association, and she doesn't have time to do both jobs at the same time. It's just that doing it all at the same time coordinated well.

Aqua is heaven
Yes, this kind of notion is very popular among anime-fans, but think of it: Aqua is depicted as a paradise. The city of Neo-Venezia is absolutely gorgeous without the danger of disappearing under the sea. All the people in it are kind and helpful (don't forget beautiful!), without being dull. Life on Aqua is easy-going, yet filled with lots of distractions and wonder, so it doesn't get boring for its inhabitants. The protagonist never returns to Man-Home even once throughout the series, nor does she long to--and none of the other undines seem to do so either. Nobody ages, even though about 3 years pass in the course of the series, which is especially noticeable in the case of Alice, who seems to remain 14 forever.

The tourists could be spirits passing through to their own ultimate destination, in a limbo sort of way. Akari and the other undines received special treatment because they were good people in their previous lives, so they get rewarded by being spirit-guides in the afterlife. The presidents of the various companies are spiritual overseers, disguised as cats. Ai could be an angel, mediating between the two worlds, until she has shown to be worthy enough to be a guide herself.

The person Alicia marries is Akino
It is never mentioned who Alicia marries in the end. The only person who is ever seen with her after her marriage is "Grandma" Akino, Alicia's former mentor. It's not so far-fetched, if you consider how heartbroken Alicia was when Akino left her to her own devices. Of course, this means that Aqua would have laws that allow same-gender marriages, but since this is an open-minded futuristic society this may very well be the case.

It could be that Alicia seized Akari's promotion to Prima as a chance to step down as an undine and be with her beloved Akino once more. Alicia likely had some difficulty with her plan once she started to care deeply for Akari as well, which might be the reason the postponed Akari's promotion--but in the end she made the decision she considered best for both herself and her protégé.

The person Alicia marries is Akira
This is slightly less likely than the previous option, considering both are never shown to be an item during the series--unless one counts the numerous occasions during which they show how much they really care for each other. They share the same age and status though, and they have very complementary personalities, although a marriage between them would without doubt be a rather tumultuous one.

Alicia is about 35 years old in Manhome time
Alicia from ARIA is 19 years old and pretty much looks that way. It doesn't gel well though with her supposed extensive experience as an undine, which led to her legendary status. It is also said that she waited a long time before she accepted an apprentice--but if she became a Prima at 16, 3 years is really not that much time. Besides, at 19 she would perhaps be bit young to retire and get married. It all makes sense if her age is actually expressed in Mars years, which means she is closer to 35 in earth time (and in some anime episodes she does look quite a bit older wen she's tired). Of course, at 35 she is still too young to retire, but she merely stops with her hard work as an undine and starts working at the tourist office. It also explains why Alicia is reluctant to get closer to the much younger Akari, despite their emotional connection.

The same holds true for the other Water Faeries, of course--Aqua's atmosphere obviously helps someone to remain youthful for a long period of time. Or it could simply be a case of Generic Cuteness. The only problem with this is the story of Akira and Aika, since Akira had still not promoted when she met Aika, who was about 6 earth years old at the time. That means that Akira (and the other two) would have been about 25 by then in earth years, which doesn't seem quite right.


 * Additional problem one with this theory: everyone else on Aqua (including 14-year-old Alice, in 9th grade) counts their ages in Manhome years -- this is explicit in the manga, where birthdays are twice a Martian year. Additional problem two: Alicia isn't 19 when she retires, but only when Akari joins the Company -- once you add up the series time, Alicia retires at 23 or 24. (Paying attention to ostensible time has its own problems of course, as Alice spends three years in 9th grade.)
 * It's still a bit early to retire when you're 23, but perhaps Alicia simply didn't like her job. Also, nobody appears to age within that time period.
 * The idea of Alicia not liking her job seems surprising considering the advice that Akino (grandma) apparently gave her, which is to "enjoy everything" (remember near the middle of Animation?) which makes it seem odd she'd retire long after that advice.

Extreme aging-prevention has been achieved
Specifically, enough to allow for the flooding of a planet, building of a city (to some extent) and ecosystems' development, all within just 4 generations. I estimate that in fact the average lifespan is around 160 years, allowing 10 years (Aika's coming of age) to pass without Alicia getting older.

It's a combination of factors
Everyone here is partially right. Aqua is a healthy place to live, medical advances have allowed for longer and healthier adult lives (including fertility, so no rush), and time reckoning reflects the longer year of Aqua AND Manhome-standard time (MST)- we just aren't told about the switchover in conversation. Thus, Alice is 14 in MST, Alicia is said to be without an apprentice for 7-8 years MST, about 4 Aqua years, and Alicia is about 36 in MST when Akira arrives and 15 in MST when promoted (The big gap there is the writers fault, they underestimated how long she had no apprentice). Akino is at least 80 MST. Any inconsistencies I blame on the writers, bad math and women lying about their age.

They did do the research on the moons

 * In order to provide tidal pull the terraformers of Aqua dragged a couple other solar system objects into orbit of Mars, maybe Ceres and one of the Jovian moons, or 2 of the Jovian moons, or maybe a couple Kuiper belt objects.

The one Alicia marries is Cait Sith
They know each other, so when Akari told Alicia about her encounters, she wasn't surprised at all. To help Akari grow up, Cait Sith planned to leave first, then wait a while for Alicia to join him.
 * Based on the last chapter, Cait Sith is also probably the one who recommended Akari to Alicia.
 * Akari's "e-mails" were shown, right after that page,

The Mars Cats (including President Aria and Caith Sith) aren't genetically modified terran cats, but the last survivors of a telepathic Martian race
The concept of them being genetically engineered housecats with human intelligence is just an urban legend. They appeared on Mars during the terraforming, and no one really knows where they came from. All of the strange things that happen to Akari over the course of the series are results of telepathic contact with one of the cats. The cats are actually benevolent, and want to thank humanity for bringing life back to their world.

Alicia is drunk ALL the time.
It explains a lot about her mannerisms.

ARIA takes place in the same timeline as Yokohama Kaidashi Kikou after humanity abandoned Earth for Mars
The Earth was in decline and considered no longer viable, so the humans terraformed Mars into a water planet and moved there. They left behind those humans who wished to stay and a few robots to look after the Earth and perhaps one day restore it to its former glory. Hmmm, sounds kinda familiar....
 * This is a little doubtful, as the series implies quite strongly that Aqua (Mars) is a tourist destination for regular visitors from Manhome (Earth), those visitors choose to return to Earth after their visits, and Aqua's population is still small and the Terraforming process not quite complete yet. Plus, there's regular contact between the main character and a little girl on Earth, who not only seems perfectly healthy and hapy, but whose parents are quite happy to return her to Earth with them without so much as suggesting Aria take their child in, since if Earth's in the state the above troper suggests, they'd be pretty irresponsible parents to want to keep their daughter there. Still, it is admittedly implied that Earth is in a pretty polluted, if still liveable state.
 * Even if the two worlds don't mesh perfectly, the tone of the two series and the fact that Choro Club did the music to both anime series makes me think there at least ought to be something to this, even if there's not.
 * Earth is viable, and humans are still having children, just not enough children so the population is shrinking. But with robots and nigh post-scarcity tech and advanced genetic engineering (cats on Mars, lots of weird things in YKK) Mars got terraformed (extravagantly) and settled. Lots of people on Mars and Earth are deliberately ignorant, leaving them susceptible to wonder at the tricks behind-the-scenes people and robots pull for their entertainment. Though this won't explain the time travel episode.

ARIA is set in the Doctor Who universe, with Aqua becoming Saturnyne in the distant future.
It helps explain why the Vampires of Venice settled on Venice after their planet was lost to the Cracks.