Welcome to the world of conures! Known for their nippy beak communication and loveable disposition. If you take him out when he screams, you are currently reinforcing screaming behaviour. We have many threads on preventing screaming and why birds scream, though I'm on my phone and I can't pull them up at this moment. If you continue to reinforce this, you're going to have a bird that screams constantly and it will eventually drive you insane
Biting is normally done to communicate, and there are many different bites with different meanings. Is he by a window when you take him out? Is he completely stream lined (flat feathers all over his body) and are his eyes opened widely? Is he fluffed up? Are you simply taking the bite without reaction? I ask these questions because they could all mean very different things. Birds don't exactly feel "remorse" per se for biting, but they can definitely associate that when they bite you it can lead to things they don't like, such as being placed back in their cage and without any contact with their flock. Some birds have been reinforced to bite because no one is "listening" to their body language, and the only way to get their point across is with their beak. They also use different pressures to communicate different things - Avery will give me:
- "hey, stop petting me" bite,
- "how dare you pay attention to someone other than me?!" bite,
- "move your hand, I need to preen there" bite,
- "I want to go over there" bite,
- "I'm exceptionally angry with you, LEAVE ME ALONE!" bite,
... the list goes on.
So more than just "he's biting me", we need "this is how and when he's biting me" to be of use. Personally I take a very strong no-bite policy with my birds. If they bite me, and HARD, and I did NOT deserve it (99% of the time we do because we aren't paying attention to them - dogs snarl, birds have a million ways to snarl), they go in the cage and they don't get any time with me for the next hour. I used to only do 5-10 minutes, then 30 minutes, and now I've progressed to an hour. Mainly because I need time to recollect myself when I'm bitten hard and because they need time to cool down and brush it off too so we can start anew.
If they bite me on the face/lips/ears, then absolutely NO shoulder privileges until proven trustworthy. If they try to get up there and they aren't allowed, I simply put a towel around my hand and "swipe" them off towards my couch. Avery wasn't allowed on my shoulder for about 4 months because she was too unpredictable. Now she's predictable (and hormones are over), so she's allowed up there when she's in a good mood. Once they've been "swiped" off (they are fully flighted so they fly down) I have them step up on to my hand and I put them on their cage. Alternatively, you can use a dowel or rope perch and have them step up onto that and place them elsewhere if they're on your shoulder. Young birds will almost always go for shoulders because they are either scared of hands or view it as a safe and high place to be. It took about a month with Shiko and Avery each to have them stay on my hand. You can also teach your new GCC to "stay" on your hand and reward him for staying - I did this with my IRN because he's very food motivated.