Is it safe for me to give my boyfriend head?

Cold sores are less likely to be passed when you don't have any signs or symptoms of a cold sore. Wait at least a week after the cold sore heals. You won't ever really be safe but when you're in between break outs the chances of passing oral herpes on when you're in between break outs is very small.
The fastest way to get rid of cold sores is to use over the counter cold sore creams or take antiviral medication. There is no cure for it but there are treatments for the break outs.

No it's not safe, but you might be able to do it while he is wearing a condom, but I don't know and I bet it is just as gross as it sounds. Don't do it.

It won't ever really be safe on its own, no - I would talk to your doctor though to see i they have any medicine or anything else that might help make it safe.

You are not contagious at a certain point, but just before you have cold sores you ARE contagious, and you may not really be able to tell until a bit after you're contagious, as I understand it.