From the head shape, it is NOT a rattlesnake. that means it's a beneficial snake that will eat mice and voles and other pests.

Yes, it is a Florida Pinesnake (Pituophis melanoleucus mugitus). Not a common sight.

Yes, it's a juvenile Black Rat Snake(Pantherophis obsoletta), a totally harmless and very beneficial snake to have around. He'll be your first line of defense at keeping rodents out of the basement.

You correctly ID'd the one at the top of the photo as an Eastern Garter(Thamnophis sirtalis sirtalis). The dark one at the bottom of the photo is a young Black Rat Snake(Pantherophis obsoletta). Black Rats don't hatch out black; they enter the world as a silvery-gray snake with a bold pattern of black blotches and lines, and gradually turn darker with each skin shed. This snake is still fairly young, as you can still see its blotched pattern visible, like the spots on a black leopard. Where you live, adult Black Rats usually are jet black with white undersides and throats, although in many places throughout their range, they will keep at least some visible dorsal pattern throughout their lives. I'm guessing that with different species coming into the basement, species with very different feeding habits, they are preparing to hibernate there. Both of these snakes are harmless, and will leave come spring. The presence of the Black Rats could be a deterrent for rodents to enter your home during winter.