Well, you've identified it correctly ...a finish mower. Presumably it's connected to your PTO, so to use it your RPMs should nominally be set at 540rpm. It should be adjusted for height of cut by moving spacers on wheel shanks above or below their respective "receivers" ...don't scalp the lawn ...and, presumably it has an "anti-scalp" roller on the front?
As for turning when mowing normally, sure, turn w. mower on ground ...but don't turn too sharply or you can easily unseat the tires from the rims and, incidentally, the tires should be checked and filled each time you mow ...probably 50-60 psi, whatever is max pressure on the tire.
The exception to the mower-on-the-ground rule is never, never back up with the mower on the ground ...because of the caster on the wheels, this puts strong, undesirable forces on the wheels and is probably the best way to roll the tire off the bead, which is highly undesireable (been there, done that ...learn how to put a cinch-strap around the tire to re-inflate/re-seat). Flat tires are a pain and if you have thorns, nails, etc. you might want to put flat proofing goop in the tires ...after the first few flats.
Presumably the top link (and, for that matter, the side links) on the mower swing, so that the mower can be compliant with uneven terrain (within limits). Mowers can eject deadly things at high speed so know who/what is in the discharge path.
When turning, note that the mower in the rear describes a broader arc than the rear wheels (just like your loader does in the front).
One other thing: if you mow down steep slopes 4wd is a must ...when you lower the mower to cut, it takes that counterbalancing rear weight off the rear tires, and can unload them enough so they have no traction ...and you have no braking, engine-wise or otherwise unless you are in 4wd (been there, done that ...a "Nantucket sleigh ride" ...it is counter-intuitive, but if you find yourself in this position, RAISE the mower)
Yet one other caution: when the mower is raised and engaged (i.e., turning, say, when you are backing up or turning sharply) you don't want it too high so that the PTO shaft angle is too severe because universal joints don't like this much.