welcome to your GCC
Yes they learn to use that beak .
For getting off head. I would hold an envelope in your left hand almost at arms length, and offer your right hand to step up. The uncertainty of the strange object should make them want to retreat to the safety of your hand. Then drop the envelope and praise praise praise.
I used to have a "naughty " flag, a tiny American flag. I would I would hold up to make mine get off my head. It worked very well, to the point I could walk towards were I had the flag and nit pick it up and she would jump off my head. So this might work fir you.
GCC will switch from love to I will bite and back to love quickly.. if you pay attention to body language, pause. You can usually avoid any bites. My girl offers to bite me nearly every day, but I avoid bites. She thinks my hand moved to fast, or I bumped a feather and was trying to kill her...whatever it is that has her on the defensive.. but I apologize, give her a few seconds to compose herself and we go on like no big deal. There are times that if she is just to wound up, she knows I say no, if that does not work its off to the cage for five minutes. Much longer than that and they loose the connection to the action.
Most of us treat bites as our fault, and missed ques. If you work from that angle you will reduce bites.
Also they can get over stimulated, or if you have had them with you fir sn hour they need a snack break and drink. Birds eat little bits all day long, so they are always flight ready. Instead of big meals at one time. Inker a snack dish near me for mine.
Also baby birds tolerate everything...but as they become adults they expect us to be more respectful, and aware they are their own selves. GCC run a tight ship! They expect you to tie the line.
They can like any parrot start to be cage protective, that's a hardwired behavior to defend the nest/territory . So just having them come out of the cage first makes everything better. Just keep in mind that's not a bird that's mean or doesn't like you. It's just defensive of the cage. My GCC is to some extent, my quakers are very cage defensive. If I tried to put my hand inside the quaker cage its screaming attacks, while if I let them step out its kisses and snuggle. This can happen after they become adults or during the spring and fall breeding season then disappear during the rest of the year.
Birds like routine. Use the same phrase, be consistent. Make sure they have plenty of out of cage time, 4 hours or more, one on one time with your attention 30 mins at least daily . Provide mental stimulation, foraging together, very simple tricks, foraging on their own. Watch bird tricks video on you tube, they have a few really great foraging teaching videos.
I highly recommend having a digital scale and weigh your bird weekly. All birds will hide being sick or health issues as long as they can. By picking up issues by a drop in weight early, and getting them to the vet before " sick" bird symptoms ( which by that point they are critically ill) they are able to recover quickly most of the time. It has been a true life saver for me and mine!!
Nibbles is the best though and I love thay he is comfortable with all 3 of us. I am so pleased that I joined this forum though! Super helpful group and really friendly. 
