The time for academy signing is the same as free agency. 5 max offers for first 2 days. No limit after that. Doesn't count towards cap. Note you can offer them a 2 year academy deal or a first team contract following this:

Academy contracts by age:

Age 18: 3y/$3m

Age 19: 4y/$4m

Age 20: 4y/$5m

Age 21: 4y/$6m

Age 22: 4y/$7m

Sheet for prospects: https://docs.google.com/spreadsheets/d/1aBSGyirYO-I4kxtkuO4rlvs4_MCibm5THPPWfANL5V0/edit?gid=81642447#gid=81642447

Here is sheet with some prospects: