Nginx should be faster in theory, but it's kind of hard to show in practice as the actual http parsing is just so much faster than anything else. You have to really tune them for for benchmark scenarios to see any kind of difference.

What your vendor supports and what you are most comfortable with configuring should decide which one you run.

PHP, as you say, is something else entirely. It's so much slower than your http server so the latter doesn't matter at all.

Not all the time... Before, when nginx was event and Apache was prefork or worker, yeah. But with the Event MPM, performance is pretty much neck-and-neck.