Mail sent through InmateAid typically takes 2 to 3 business days to travel from InmateAid's Florida office to the facility through the US Postal Service. Once it arrives, the facility mailroom staff open and inspect it before clearing it for distribution, which can add a day or several more depending on the facility. Mail call at most facilities runs Monday through Friday, so weekends do not count. Plan for the full journey from send to in-hand to take anywhere from 5 to 10 days.
Yes, the inmate can absolutely write back. All they need is paper, a pen, and a postage stamp. They address the reply to InmateAid's office in South Florida if you used the service, which keeps your home address off anything going through the facility. When the reply arrives, InmateAid scans it and posts it to your account for you to read.
If you sent the letter with your personal home address as the return, he can write back to you directly through standard mail the same way.