InmateAid pulls location data from public inmate databases, so if someone is listed at a facility there is a strong basis for that placement being current. That said, inmate databases do not always update in real time, and transfers or releases can create a lag between the actual situation and what the system shows. If you have any reason to believe the location may have changed, confirming directly with the facility or through the relevant DOC's inmate locator is worth doing before sending additional mail.
Assuming the location is current, your letter will go out to that facility through the US Postal Service and should reach your inmate within about a week after it is processed and sent by InmateAid.
On cost to the inmate, the service is completely free on their end. They do not pay anything to receive your letters and they do not need an account. InmateAid is entirely a service for the person on the outside.
For the inmate to write back, they simply address a reply to InmateAid's Florida address, which appears on every envelope you send, and mail it out through the facility's regular outgoing mail using a postage stamp. When that letter arrives at InmateAid it gets scanned into your account and you receive a notification. The incoming letter fee is $1.99.
How quickly they respond is entirely up to them. InmateAid has no control over whether or when an inmate decides to write back. That part depends on the person.