Does House kill himself?

I think it's just a reminder that Wilson will die, and that it is inevitable.

It is left in the open what he will do, and left to interpretation. After doing this selfless act for someone, I'm guessing you can follow two approaches:

• He won't have any other reason to live after Wilson

• He is selfless and can try to help other people he cares about or meets meanwhile

I believe the second approach, he will explore and eventually find something else to do, simply because he is obsessive about everything. The puzzle never dies.

Does this mean he's going to kill himself after Wilson dies

House is* prone to do whatever the heck he feels like at the moment, according to whatever logic he just happens to come across at the moment.

• If he encounters someone who wants to commit suicide (perhaps Wilson in pain) and House thinks that the suicider's reason is stupid, House may decide that he must live as long as he possibly can because that is the job of all living beings. If he feels that is the right thing to do, then he will see it as an imperative to do exactly that.
• If life seems pointless, House may think that a human's logic should overcome our naturally-implanted tendency to seek out life and comfort. If House's logic determines that ending life seems like the most sensible, logical thing to do, then there would be no talking him out of it. Bye bye, House.
• If he finds something else that he has to do before he offs himself, then there'd be no talking him out of that. House will pursue his own priorities.

I've found House to frequently be rather unpredictable. What he decides may be highly dependent on something that happens in his life. However, whatever he decides is something that surely* you're not going to have any say in.

 * This whole answer is predicated on what the character of House would do. In reality, history is filled with people who become enlightened, and reformed. Actually, I think that is the whole premise of the last episode. House decided that friendship has value, and he tosses aside everything in order to focus on that friendship. This is an unexpected development that we see in his life, not unlike the reformation that has happened in the lives of many other people. I'm writing this answer based on how we've seen House react throughout the series, in case House reverts a bit back to the House we know. However, if he continues to pursue a new outlook on life which re-defines his character, then House's actions will depend on just how his character changes. Therefore, his actions at a later date will be even more impossible to predict than what I've already stated. This only underscores my point that the answer boils down to:

There's no way for us to know at this time.