Two molar side-by-side dental implants to be surgically placed only with a lidocaine injection. Like the one for a filling. Can I drive myself home?

Sure. No different that the anesthesia for a restoration.( As long as you don't need your mouth to drive :) ) Good Luck.
Definitely, yes. After receiving local anesthetic or nitrous oxide you can drive home or have a driver whichever is preferred. Some patients still like to have someone with them just in case they are not feeling up to driving.
Yes, you can. As long as you are licensed. You'll still be numb on the drive home.