Suppressor is form 4, correct.
1.) That is correct.
2.) That is an adapter that allows the use of an HK style quick detach method of putting your suppressor on. The other side of that equation is an adapter that attaches to the back of your suppressor; think AR15 bolt fitting into the corresponding recesses in a barrel extension. You put the adapter over the lugs, push against some spring tension, and twist about 1/4 turn; it locks in via spring tension, and the shape of the lugs.
3.) I have had very good luck with Silencerco products - if you want a dedicated pistol suppressor, the Octane series is good; if you want a more versatile option, the Hybrid allows from pistol through 45 caliber rifle (.45-70) - and pressures up to .338 Lapua w/ 18" barrel. There are very good suppressors from a lot of brands; see 3a.
3a.) You take the recommendation into your local Class3 dealer, however, keep in mind that depending on how your local dealer orders, and what companies they deal with, you might be adding a bit of time and expense. My local dealer that I prefer deals with a lot of Silencerco stuff, so he has it in hand, and at very competitive prices. If you order a silencer from on online dealer, they will have to be transferred to your local dealer, then to you. This takes time (2-4 weeks), and most places charge at least $75 for that transfer. Depending on your area, it is worth seeing what you can get in hand; if you can't find what you want, bear in mind that to actually get it into your hands will be probably another $100 with shipping and the transfer, and a few more weeks of waiting.
If I was in your shoes, I would call around, and see what you can get locally, and get the price in hand.
