Sounds like you have a pretty complex series of problems! This reply is going to be fairly long.
What kind of conure is your little girl? Different species exhibit different personalities and behaviors, so that can play a big factors in a lot of decisions.
It sounds like your conure is a good example of a bird running their own life, and doing a poor job of it. It`s going to take a lot of work to change that!
First off, it might be better off to keep your birds in neighboring cages, instead of the same cage. They could still have out time together, they can still see each other and interact, but sharing a cage with a rambunctious conure can be a little overwhelming for the more sedate and layed back cockatiel, and could be potentially dangerous to the `tiel! Your conure could inadvertantly deliver a strong bite and injure your `tiel, costing the `tiel a toe. It will also begin to acclimate your conure to the fact that no, she can`t ALWAYS be with the `tiel.
I would also begin to have training sessions where you take each bird out individually and work with it. Getting them apart from one another for brief times will help immensely. It sounds like it`ll be a relief for your `tiel to get a little one-on-one attention, and it`s something your conure needs to learn to enjoy. For your conure`s training sessions it`ll most likely be beneficial to take her into a `neutral room,` where she can`t see her cage or the `tiel, a room that she doesn`t have a strong territoriality over. Once you`ve got her in that room, the most important thing is to just have fun. Offer her favorite treats, play with her favorite toys, etc. She needs to get a little more socialized with people to help make everyone`s life a little better. Remember the point it to make her enjoy time with people, so make the time enjoyable! I also highly recommend teaching her to step-up onto a handheld perch. This will make her much easier to control for everyone else in the household. They`ll be able to safely pick her up and get her back into her cage, or get her out of her cage and into a carrying cage in the case of an emergency. The best way to teach her to step up onto a stick would probably be to let her decide to step up, rather then force her into it. Let her play with it, and whenever you see her standing on it, reward her with treats and drama. Once she figures it up she`ll step onto it readily, then you can work on picking it up, getting her to step onto the stick when it`s presented to her, carrying her around the house on the stick, etc...
To help with household relationships, try to find ways to safely and enjoyably encorporate the rest of your family into your conure`s life. One of the easiest ways is to have them provide her favorite treats like apple, or seeds, or shower time. Perhaps your conure can be taught to engage in games of tug of war with them through the bars of the cage. Or perhaps they can enjoy a rousing game of `fetch for me, slave!` or `pick up my toys, slave!` Most conures thoroughly love throwing things to the floor and making other people pick them up for them. Maybe they could try peek-a-boo? Come up with games that`ll amuse your bird and your family members, and keep all fingers safely un-bitten. The best way to stop biting problems is to avoid the situations that make them a problem. When there`s more trust built up between your family and your bird the problems with aggression should reduce dramatically. When they feel confident with it, they can try having training sessions in the neutral room with your conure.
Screaming usually becomes a problem when birds figure out that it`s a good way to get the attention they crave, even if it is someone screaming `Shut up, stupid bird!` (gosh it`s so fun and exciting to be yelled at! Did you see how dramatic he just got?!). So your conure needs to be taught that this won`t work, and that there are other ways to get attention. Your whole household has to be in on this plan, and agree to stick to it FAITHFULLY. All screaming must be completely, 100% ignored. (With the exception of saying hello when you get home, and checking if the bird sounds alarmed or hurt. She might have a foot caught in a toy!) Turn your back on her, get up and leave the room, put on earplugs. This is going to get worse before it gets better, but everyone has to stick by it. Screaming will not earn her any attention, or dramatics.
Reward her when she`s silent and good... and pick a vocal behavior that you prefer to screaming, and teach her that THAT will get your attention. Does she talk? Perhaps you can come running over to her cage every single time you hear her say hi. Soon enough she`ll learn that you ignore her for screaming, and run over when she says her sweet little `hiiiii.` Won`t that be a huge improvement? Any vocal behavior will do, it doesn`t have to be a human word by any means. You just need to teach her that that`s how she can get your attention.
Hopefully that`ll work with the food throwing too.
