By the symptoms you described your budgie is sick, you should get him to the vet so he can give him the proper medication! By giving seeds and a vegetable diet, you should also give him liquid vitamins during molt. If your budgie wants to eat pellets, get them from the pet store or order online. Good luck
I made a lot of videos about taming budgies https://youtube.com/playlist?list=PLWeRiaM2dt-kcoo8dbkd9oS5d82tPKYoq if nothing helped after all you done then your budgies may had trauma or just don’t want to be tamed
You can get another budgie, female or male budgie so your male budgie won’t be alone. They are social birds, they need the company of another budgie.
That could be many reasons, if he is not active as used to be, it is better to take your budgie to the Vet to be safe.
1. for more than 24 hours out, you will need someone to look out for your budgies. They need fresh water and food daily.
2. That’s alright, you can’t force your budgies if they don’t like fruits. Giving them green veggies once or twice a week is alright.
If you have pair of healthy bonded budgies, there will be eggs in the nest box if she is entering inside and spending some time. You can open the nest box for a quick peek when she is outside eating or resting.