Question: If a user is using their full name as their user name, what, if any, is the community standard with regards to emailing that user using their independently found work email address about their questions/answers on MO (since MO does not have a personal message feature).

I am aware that users are informed of comments on their questions and answers, but if a user is not responding to comments, is it considered "bad form" or a breach of protocol to contact them directly?

Another possible scenario: A user posts a research level question, which makes you think it possible to collaborate with that user on a paper, so you do not want to post partial results, which may lead other mathematicians to preempt your ideas (not my current situation, but as a young mathematician, I have a lot of ideas which I am sure other people could work out much faster than I can, so I can imagine this coming up).

Answer: 
I think that mathematical questions are fine (though don't pester people), but I get annoyed when I get emails about administrative issues (e.g. closures and down votes). Those should be dealt with on the site.
In fact, (and maybe I should make a separate question out of this) there probably should be an activable option to receive personal messages from other users here. Then if a user does not have this option activated you would know that this user prefers not to communicate in private.