I did some searching, and I apologize if this is covered elsewhere...

I have some flights on QR in business connecting at DOH in January:
DFW-DOH-ADL (3 hour 40 min connection)
ADL-DOH-DFW (3 hour 50 min connection)

According to their website, it is QAR 175 (about US$50) to visit the fitness center.

Provided the incoming flights are on-time (looks like they usually are, if not early), does this look like enough time to visit for a minimum of 30 min workout, then say 20 min to shower and get dressed? Say an hour for all that just to cover myself (of course I'd work out more if I could).
If there is time, I'd also visit the lounge afterwards to get something to eat.

How is security to get back into the the airport proper from the hotel?
From what I've found, I don't have to clear immigration, which saves some time.

Has anyone else done this? What were your thoughts? I'd probably swim (minimal equipment needed), and can just throw a suit, goggles, and cap (if needed) in my backpack, and I'd be set. I'll check to make sure, but I think the fitness center provides towels.

Is there anyplace airside (such as a lounge) where I could leave luggage, without having to deal with it at security? The fitness center has some sort of lockers, but not sure they would be large enough for a roller bag (that is something I'll check on). I'm debating if I'll check a bag and simply carry a backpack with me, or carry on both backpack and roller.