Should I start training my new bird now to build trust quickly?

Time, patience, and lots of treats. If you notice Curio has a favorite food, you can start by offering that favorite food only when you're interacting with him. IE, when you pet him, approach his cage, let him out, etc. This can help him to associate you with something fun/good and also make him more curious every time you come by to spend time with him. The same can also be done with toys he likes to play with. Sitting near them when he's out of the cage playing, and feeding a treat every time he comes close or shows interest in you can help teach him that you are safe to interact with and play around. If at any time Curiou becomes nervous or scared, stopping the activity and letting him calm down is best. From there, you can go back to the previous way he was OK with (IE just giving a treat from your hand but not petting) and work again from there.

I would give cookie time to acclimate to his new environment. Let him get to know you and gradually offer treats to gain his trust. Depending on how old he is and what he his previous experience and training is will help determine how quickly he may trust or learn your cues. Birds for dummies is a great book for beginning bird owners. There is lots of great behavior advice from an avian vet. Good luck! http://www.dummies.com/pets/birds/birds-for-dummies-cheat-sheet/

Thanks for reaching out about Polie. Winning the trust of a bird requires time, to decrease stress. A book entitled "A Guide to a Well Behaved Parrot" is a good start. Trimming wings might decreased the flight potential when scared. Offering treats by hand can win trust. Good luck.

Thanks for reaching out about Coco & Peach. Winning the trust of your birds will take time. Start with quiet deliberate movements, and offering treats via hand. Since many birds can be cage defensive, you might have to allow them to come out of the cage, for them to be less protective. Take the time, as trust can take some time. Good luck.

Thanks for reaching out about Pico and including pictures. Individual birds with respond differently to training techniques. Being the provider of treats and playful activities can gain trust. Letting Pico see you play with the other lovebird, and then want that same experience, might help also. This is a difficult one, because not all birds are tamable. Good luck. Be persistent.

The best thing to do is just spend time with your birds as much as you can. You can offer a treat every time you come by, or talk soothingly and quietly when you are around them to help them get used to you again. If you can't always be there paying attention to them, making sure they have other enrichment such as extra toys, a playpen, treats, etc can help with boredom.

It sounds like Rio is still getting use to his environment. I would recommend finding a treat he really likes. Than you can give that treat to him by hand to help build a bond/relationship. If he does not settle down soon I would get a slightly bigger cage.