Interesting idea. The mission prompts were fantastic and the different versions of immortality are very gameable. The mechanics need some tweaking though. The team trait doesn't feel necessary; it's a free ability that could invalidate some PC concepts.
The shared costs also felt unbalanced with the consequences unclear. Is it three deaths per squad or per character, and why are some options game-ending? Good ideas but it might benefit from play testing. Bonus points for presentation and the extra trait options.