The rationale behind putting the hitboxes on the lower halves is that the weak point is the nuclear reactor powering the whirr suits... since everyone using a whirr suit shoots from the reactor, the hitbox basically is centered from a mechanical point of view, there's just a lot of irrelevant character fluff sticking out on top of the sprite. (There's a handful of characters where a very disjoint hitbox is a deliberate part of the balancing, most notably False Queen Eli and Shield Anikel)
After dying, you will respawn in basically the exact same screen position you were when you died... it's clamped a bit so you can't get too close to the screen edges (in particular the left edge), but essentially you can just keep staring at the same position to figure out where you will respawn.
Picking up treasure items (the stuff that drops from chests and powerful enemies) refills the combo timer, this also temporarily stops the combo from dropping if the timer has run out. Powerful treasure (the stuff from blue chests) also add 0.1x to the combo. So it's basically all about points, it's just more complicated than "get things for points". The idea is that you'd strategically pick up treasure at the last second to prevent your combo from dropping when there's an enemy drought, so you can maintain that juicy 10x combo through the entire stage.
You get extra lives from stars, so those have a purpose beyond points. (Larger stars are worth more points and more star value). Killing an enemy turns all their active bullets into stars so there's strategy involved in that too.