Why is my budgie running back and forth and chirping? Is it normal?

It sounds like Cheeko may just be excited and enjoys getting out and exploring. Singing and chirping can be signs that he's enjoying his time. Offering some fun toys to play with and safe things to explore may help encourage this behavior. As for things to give when he does something you like, a favorite treat such as a piece of fruit (apple or strawberry slices are always favorites, or even a piece of lettuce or spinach!) can reward him. You can also find many commercial bird treats at your local pet store that are safe to give.

Congratulations on your new birds! If the flying back and forth is in response to when you are putting your hand into the cage this could be due to fear or being startled. If he is randomly flying throughout the day with no relation to you approaching then it could be him just exercising. Millett is a treat that is very useful in helping gain your budgie's favor as well, so letting them nibble some from your hand or while you touch them if they are comfortable with you touching is helpful in making interaction with you a pleasant experience and can eventually be used to lure them onto your finger or hand!

It might be that he's not actually completely asleep, or he's just having a good dream! If he's otherwise healthy, active and normal, I wouldn't be too concerned. However, if you are seeing any signs of illness while he is awake such as lethargy, puffed feathers, not wanting to eat or drink, trouble breathing, etc, then this may be a sign there is something underlying which should be checked out by a vet.

If Floki is otherwise happy, active, eating and drinking, and growing, I wouldn't be too concerned. Birds are very active and lively, and it could be that Floki is showing you his excitement. Spending some time together bonding, or offering a fun toy he can play with may help. If he does show any signs of illness with this, becomes listless, or otherwise seems very stressed out, a vet visit to rule out any health issues is always a good idea.

He could just be bored or stretching. Giving him time outside of his cage to exercise, as well as providing plenty of enrichment such as toys, treats, time together, etc can help keep him in shape and reduce boredom.

That just sounds like a relaxation behavior or possibly adjusting the food in her crop, and is very normal. As long as Juno is otherwise healthy, active, and happy, I would not be too concerned. If she shows any signs of illness in addition to this, seems in distress, or does it constantly without stopping, seeking a vet exam in person is always best.

I'm sorry to hear about Blue! If moving his cage to a quieter area or covering it for a bit doesn't help him to relax, or he seems to be showing signs of illness in addition to the sudden pacing, seeking veterinary care in person to rule out any health issues is best.