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: 
To my knowledge, there is no spoken standard followed by the community.
There are general rules of politeness and courtesy: applied here, they suggest
to me at most one unsolicited comment and one unsolicited email per MO
question. If you don't get a response after (say) three attempts, drop that form
of contact with the MO user. You can try using the chat feature, but you have
to monitor the other user's page; it can seem like stalking if done poorly, so
be careful. Note also that the user name may actually not be the name of the
person using the account.
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.