The Meek/WMG

Soli will encounter some kind of supernatural creature

Both of the previous chapters have had a phenomenally powerful (and maddeningly enigmatic) supernatural creature; we can assume Mocheril is a Big Good while the Dagre is a Big Bad. Before this current chapter (chapter 3) is finished, Soli will meet with a third creature, on a level to the previous two but allied with neither; possibly an incarnation of Chaos or Freedom. It will recognize and/or dub Soli to be "The Center."

Jossed. Chapter 3 has now started and no giant floating monster.

About a year ago, Pinter suffered a significant head wound.

This image (taken from the author's tumblr) shows that as little as a year ago, Pinter was, frankly, a fine specimen of manhood. Since then, he's not only let himself go, but become an alcoholic and developed a memory problem. So, a year before the events of the comic, Pinter suffered a severe head trauma that may have gotten him discharged from the army. (The fact that Amen as-of-a-year-ago is depicted suggests that maybe Amen and the mysterious third man were present at this event.) The only medicine available was cheap alcohol, to which Pinter became addicted. Now, though he's mostly healed, he still has significant memory loss (why he got "lost" on his expedition, yet flatly denies that he is lost) and fell out of shape.

Alternately, it could all be the booze.

Soli is a time traveler

I don't have much proof, it's just a hunch. A giant bird will be involved of course.

The Dagre murdered Phe.

The ambassadors of Caris had no reason to murder Phe. It would offer no political advantage: it seems the only possible outcome is that the hair-trigger temper Emperor is determined to declare war on their country. The Dagre (or is it just Dagre?) murdered Phe (by magic) and made it look like poisoning, because although the Dagre acts like he's on Luca's side, all that he wants is to see all humans eliminated, and an international war is the best way to do it.