Theory of Evolution
It will complete the tech you have selected when it is built, then will allow you to choose your next tech, which it will immediately give you also, then will ask for the next research item, and will leave you researching that tech with NO accumulated beakers.
SO the most efficient way to use TofE is:
1. Complete research on current tech. Select the first tech you want TofE to give you. Set research to 0%.
2. Complete Tof E. Get the 2 free techs you want, with no wasted beakers.
3. Selected the next tech for normal research and set slider back to a sensible percentage.
Since research happens BEFORE builds, IIRC, you can even complete your research on the turn the TofE builds, but I sometimes play it safe and give myself a one turn buffer anyway.
Respawn
My understanding is that AI civs will respawn when killed indefinitely. Provides there is an unexplored area of the map sufficiently far from other civs a new version of the civ will start.