I agree with your answers but 3. there is a reason why almost every endless high score chasing games have extra life feature since pinball machines, it makes the game more fun as it encourages the player to make the game last longer. the descent creator's new 6DOF shooter Overload also has endless survival mode and it continously gives health points for killing enemies, but it's never easy to survive more than 10 minutes.
My excuse for not doing the same is that it would make balancing the difficulty more complicated. I will have to do some more testing on this.
It might be a good idea to add a possibility to regain some amount of health along the way, I would just have to adjust the difficulty to compensate for this. Randomly appearing rare health power-ups are not an option because that would introduce too much randomness to player's success and final score. Perhaps the enemies could drop items that would give a minimal amount of health to player. But this should only happen in certain conditions..
The end of the level would be a good place to reward player but I'm not too keen on using time as the condition. I have so far intentionally avoided all time limits and time rewards. Also, determining the actual time limit for the reward would be tricky because the levels are procedurally generated and unique.
Someone suggested simply restoring the health to some minimum value on level completion/start, so that the a level would never start with near-zero health. I kind of like this idea but perhaps I should limit the total number of times the health would be restored.