I cannot find any regulation on this, so how far out can active duty who are separating from the military apply for federal service jobs?

I think you can apply whenever you see the job posting, but I don't think you can start work until you've separated. For instance on all the job postings I submitted, one of the main questions was "When do you start Terminal Leave" and "When is your EAS date". Because I took a full 2 months of Terminal, I was available to work right away.

Staff, there is no regulation on when you can start applying. I would say start applying 6 to 8 months from separation.

It would depend, if you are applying for a federal job and you have 6 months to go it may be enough time, and it may be too much depending how the HR section handling your packet works. It is not uncommon to hear of people taking 6-months to a year. and three months is fast.