Unless you have a really weird utility function that values voting in and of itself, what matters is the outcome of your vote.
Not at all. My utility function might value my self-perception as a person who votes for X. It might value the ability to rant about how I did or did not vote for X and therefore all the bad policies are not my responsibility -- if only they have listened to me! It might value the warm glow of having done my civic duty of helping the forces of light triumph over the spawn of evil. Etc, etc. None of this is particularly weird.
I would argue all those values are irrational. Ticking a box that has no effect on the world, and that no one will ever know about, should not matter. And I don't think many people would claim that they value that, if they accepted that premise. I think people value voting because they don't accept that premise, and think there is some value in their vote.
If there's such a small chance of your vote making a difference in the election, you should be comfortable voting for trump.