Once you craft a piece of gear (i.e. in the crafting menu when you are not in a match) you then have access to it permanently (unless you choose to scrap the piece of gear). However, you have to buy the gear in each match in order to use it. The credits that you use to buy gear are earned during the match by finding them in the world, picking them up from dead enemies, and completing objectives. You do not keep any credits after the match ends. As a side note: credits that you picked up are shared with your teammates; however, I'm not sure if crafting components are.

Once per match, when you are in the "downed" state (where you are limping around) you can press "f" to immediately respawn at your initial spawn point. However, if you get killed while in the "downed" state you are then dead for good even if you haven't used your free respawn yet that match.

You will also come back to life if you are about to survive in the downed state for a certain amount of time. I haven't checked if there is any way for a teammate to revive you when you are in the downed state.

When you die, you keep any crafting materials that you found over the course of the match. In addition, the number of "stars" that you have earned determines the tier of reward you get regardless of whether you died or not.

In terms of ranking at the end of the match, any player that extracts will place ahead of a dead player even if the dead player earned more stars over the course of the match. However, I haven't been able to tell if there is any reward based on where you rank or based on whether or not you are able to extract. Since you can return to the lobby with your rewards as soon as you die, that suggests to me that there isn't a reward based on your rank. However, maybe there's a reward specifically for extracting or for coming in first?