Hello and welcome.
I thin you really need to bring some new birds in with your cockatiels to sort out the bloodlines. Looking at the photos I can see the ones that have had some feathers puled out but there's also some really nice ones too. Is it possible to trade some of these? What you really want is to get your ratio male to female more even.
I also feel you need to keep your cockatiels and budgies separate especially when they are all breeding. If possible can you build some single pair breeding cages for the cockatiels and budgies. That way you know who is with who and it helps to stop the fighting and any future in breeding. Cockatiels don't particularly care who they're making babies with as far as family.
The problem you've run into is one I had myself in my teens. I now breed pairs in their own separate aviaries. I just rotate them through the breeding aviaries so that the parents only have 2 clutches a year. I think this is better for the health of the parent birds. If the parent birds are healthy then chances are better that the babies will also be healthy.
If you have more questions on breeding then there's a section here that would be better for you to ask in
Aviaries & Breeders - BirdBoard.Com - Parrot Message Board & Pet Bird Owner Forums
Also the cockatiel area or budgie area.
I have no experience with finches or canaries.