Nothing is permanent across runs except unlocked items/enemies that can then seed in item pools. So for instance, X item doesn't show up until you achieve Y objective in a run, but then it starts showing up in other circumstances earlier, etc. Same with enemies.
In terms of you losing stuff when you take damage, that's not particularly the plan at the moment, although there might be some sort of item that plays with that concept, who knows. Overall this is a lot more like Isaac where you're collecting things constantly as you go through the run, and you either make it or don't. The big choice you have is which things to take at any given point, though. There's a lot more in terms of choice of weapons and whatnot to take with you, and Dayton and I have discussed having an MMO-like quality system on them as well to help broaden the choices you're likely to make with them. Not positive if we'll do that right now, though.
There are a number of games that we take inspiration from, both positively and negatively (what we like about them and what we want to avoid that they did). The progression through runs is something that Isaac does well, although it can be sparse at times. Rogue Legacy handles the meta aspect well, but the during-run progression is really dull. Traditional SHMUPs really use a system of very temporarily holding an upgrade, etc.
Oh! I forgot. One sub-category of items that we have planned (and the code is already there for) are ones that have "probations" on them. Basically those are things that you can't do if you want to keep the item, and you lose the item if you do the thinig. One might be firing a missile, or taking damage, or whatever. In some cases a probation is a temporary thing, lasting only until the next floor. So basically "this weapon is yours for good if you manage to go the rest of the floor without taking damage." So yeah, there's a variety of stuff that actually does fit that model.
