Short answer: No, no happy endings, with the possible exception of Markus' special ending. But you stay alive in most endings.
Long answer: If you get shot, it means that you choose a faction that doesn't like/trust you enough to save you. If you made a deal with Lazarus, he will indeed aid you, but not at this point, but rather in the final battle. (He also will go after Andrei and might even succeed onscreen, depending on you choices.) If you have enough influence with the faction of your choice, you will be saved by that faction and you will make it through the story alive. As for the mentors, there are no ways to "fix" Heath or Randal or even just keeping them from getting worse, though there are endings where they stay with you. Markus' endings are not quite that gloomy, though I found them still pretty depressing, with the exception of his special ending, as already mentioned.
PS: I definitely didn't feel like the game endorses drugs, quite the opposite. That Heath tries to escape from reality and numbs himself is actually his fatal flaw. Mind you, you don't have to sleep with him, and you can also just pretend to take the drugs, if you don't mind deceiving him.