Hitboxes are in fact not boxes at all, but are pixel perfect.
Unknown. NOT pixel perfect, we don't think.
Warriors and Queens have a second hit "box", their weapon, which is also pixel perfect. This hitbox, as you might expect, behaves differently from their body, and attacks that hit it before their body will bounce off. However, this hitbox only exists while attacking, and for gun warriors, is considered to be the laser, rather than the gun itself.
Fairly certain NOT pixel-perfect.
The servers are the single source of truth when it comes to gamestate. Sometimes, your local client will be "behind" the server with respect to the picture you see (the victory hex, for every purpose presumably other than the That's Amore victory condition, is based on your client rather than the server). In this case, it can lead to confusing win-state portraits which seem to be "wrong", especially for military victories where the queen and her killer have a large ping gap.