Disease is 1000x less likely if you are breeding your own fish versus buying feeders from a store. As per how long until you can feed the fish - it depends how big the pirahnas like there food
The one thing I do see is that you mentioned a 10g.. I'd personally recommend a 30g for breeding convicts, but I tend to under stock (with the exception of my mbuna tank), so a 20g is probably the more acceptable size I'd expect to hear from others around here.
I'd suggest a 3rd 20g. Breed in the 20g, move the fry at a big enough size to sustain themselves to the 10g, quarantine for a week before feeding to make sure there is no disease/issues with them (although, there shouldn't be considering the parents are healthy, and some might say this is an unnecessary extra step).
Typically, it being your own tank though, diseases are much more controllable if you take care of the tank. The person who has been helping me out with my tanks had 1 problem, ever. And that was after neglecting to quarantine new fish (admittedly, not many of us do with freshwater).