We have had birds most of my life. I had parakeets as a child and cockatiels and parakeets as an adult.
You are right. You need to seperate them and put them in differant rooms. To teach him not to bite you need to start with talking to him for several mins many times through out the day. Try offering him a cracker through the bars of his cage. Set one in the corner where you can wedge it between the bars. I can give you a couple of other ways to offer one later. Continue to offer a cracker every day. Talk to him all the time and never ever put your hand above him. That will frighten him. Move slowly and deliberately when you work with him doing anything for him. He has to learn to trust you. Talk softly and maybe even singsongy like you would a baby.
Keep your hands out of the cage if you can. Do you have a cage where you can push the feed cup in from the outside of the cage? The less you invade his space the more you will minimize his fear. You need to build trust with him first before you can handle him. If some big hand came out of the blue at you wouldn't you be afraid?
You need to take baby steps in reaching out to him. Does he have lots of toys? If he is bored he will be more aggressive. Birds are VERY territorial so you need to learn to read his signs and respond accordingly. A bird who is clicking and hissing is the same as a dog growling. A dog low growls before he will lunge. A bird will make similar sounds before attacking. A bite can be of various strengths depending on what the bird is trying to tell you. You need to learn what your bird is saying. Then you can respond.
If he is warning you sometimes they will pluck the bars of the cage like a quitar string. that means he feels threatened. Soothe him with baby talk and back off for a bit then try again to move slowly toward whatever you were trying to do. Our present cockatiel will still bite but she only nibbles now. But they can really take a chunk out if you don't respect their space.
There is alot more I can tell you if you want more.
Do you keep your fingers tucked in away from him when your hand is in the cage? They generally will not attack the arm but will go for the fingers. so if you protect and hide your fingers he shouldn't bite provided you aren't crowding him.