There are about 1.25 Million Acres of public land in the Black Hills. About 80% of that is on the SD side. There are scattered patches of private land in the Hills, but there are maps available from the USFS showing where those private patches are.
The deer population (and ungulates, in general) here has taken a hard hit from mtn. lion predation, but last summer/fall there was pretty severe drought. Blue tongue knocked the deer down even more. There are still enough deer to go around though, and it is pretty much a do it yourself thing. Paid outfitters are not permitted to guide on the public lands here, though I'm not sure if that is a state regulation or not.
As for 4-Wheelers/ATV's etc... Pick your poison. They must be licensed, street legal, and remain on designated roads (either public roads, or USFS roads with the 3-digit roadway signs). If you are caught off of designated roads, they will confiscate and cite you. If you are turned in for being off the designated roads, you will probably be cited. If you are on USFS designated trails (those USFS two-tracks with a 4-digit marker), you need to have a "trail" permit. If you take your 4-wheeler off road, and screw up someone else's hunt, Lord only knows what they will do... Some guys aren't very forgiving in that regard.
FWIW, the archery deer season coincides with the Rifle Elk season, so chances of running across other hunters is fair - - depending on which areas you are in.
The local custom in the Hills is to park at or near the head of a USFS Road intersection... That should be an indication to other hunters you are in that area, and they generally move along and leave you unmolested. However, given the number of East River folks (from eastern SD), and the number of out-of-staters that have been flocking here, that custom isn't followed, except by the locals. If you do come this way, and if you park at or near an otherwise unclaimed patch, then take off to hunt, but remain within eyesight of your rig, you will be able to pick the locals from the yay-hoos by who keeps on going.
With regard to camping, remote camping is allowed anywhere in the Black Hills, so long as you aren't in the same area for more than two weeks. If you do camp remote, you won't be able to have any open fire at all. Only camp stoves, etc. You will need to follow up on the specifics of that regulation. There are campgrounds scattered throughout the Hills, and there is a daily fee - - those are first come, first served. But, the good news is they generally have approved fire-pits for open fires, provided a special fire ban or restriction isn't in place. One other thing... If you burn wood, get the wood locally. If you bring wood in with you from out-of-state, that's a No-No...
Not sure what else to tell you at this piont, but keep us posted, and maybe we'll cross paths.