This is the way I have bred my carpets.. many ppl use slightly to completly different method .. so as I said .. this is my oppinion.
What is the minimum size for breeding?
The smallest I have ever bred was an 18 month old (wich is very young .. generally ppl breed as of 3 years old. At 18 month old I only got 5 eggs compared to 3yo that can have a good 10-20some eggs..
What temp do they have to drop to, and for how long?
This is my way of doing it; I usually always keep a day time high of 90 through out the year but during about 3 month, I slowly decrease my night time temps from 85 down to low 70's even 68F. I then slowy raise the temps back and start some introductions.
Also do males get more aggro. than females once they reach maturity?
I would have to say that sex is not a factor as to wether a snake is aggresive or not .. In my experience.. baby irian javas are born 90% tame, almost all coastals are born tame and almost every single Jungle carpets I have ever had are born agressive.. This is from my experience though ..
What does the nesting box have to consist of and does photo period really affect anything?
The nesting box for many is a box filled with partially wet vermiculite to offer optimal laying spots although I have heard and tried myself with great success to use shreds of newspapers as an eggbox .. the only problem I had was some newspaper occasionally sticks to the eggs..
As for lighting .. some use the light cycle some don't ... I always have.. 12 hour days and down to 8 hours days during cool downs.. with slow gradual changes from one cycle to an other..
I hope this helps you a bit .. again .. this is the way I do it ..