Yes it is. Usually you want to give them time to adjust to you being gay before you tell them you're dating rather than hitting them with all of it at once. It might be a bit overwhelming to process both at the same time.
If you say you're gay, then in their minds, you're "fixable". When you start dating, then things have taken a turn for the worse.
Yes, they are completely separate. Telling your parents you're gay in no way implies that you're dating, and saying that you're dating in no way implies that the person on the other end is a guy.
When I first came out to my parents, I didn't dare mention my boyfriend. That would have set them over the edge. So yes, they're 2 separate things.
I think in most cases it would be best to tell them at separate times. One thing I have learned from the corporate world is to never just come out with with news. You should always tell them what you are going tell them so they have some time to get used to it. I think it is a bad idea to just say I'm gay and I want to bring my boyfriend over for dinner.
Absolutely different. Because (a) they can still be in denial about it if you are not dating a member of the same sex, and (b) if you're dating - even when you're hetero - that also brings up the possibility that you're having sex/engaging in sex-play, which is yet another can of worms (hopefully wearing condoms!) that parents have to deal with.
I think it is two separate things as well. You shouldn't unload too much information at once it can be way too much for people to handle. Not to mention it ruins your parents 'plan' for your life. I think it should come in the same package only if your parents sit you down and ask, (i don't like deception too much) because by asking they are at least part of the way accepting