I've got a red earred slider I rescued, and can say definitely they can feel everything. Mine particularly likes it if you use a toothbrush to scrub off scales of his shell.

Also lesser known but very important fact about aquatic turtles- they need a good place to sunbathe, something they really enjoy and helps with health. Also, room to swim (e.g. don't keep a turtle in a couple inches of water; they need depth. Mine enjoys 55 gallons to himself).

As for socializing... that parts hard to say since it's easy to anthromorphise their behavior. Are they happy to see me everyday? Absolutely. So do goldfish. Do many turtles get along? For sure, I see them stack up at the lake. Does that make them social? Who knows, but likely not in a way humans are.

Btw they make fantastic pets, just be mindful of how big they get, especially females. I had to build mine a hutch to sunbathe atop his tank, too. People often abandon them, so much so that they are illegal to sell in some places. Do keep that in mind!

Can confirm, turtles can feel through their shells. Petting or light scritches tend to be enjoyed.

case in point

Turtles love to be scratched on their shells. They frequently shed their scutes, little pieces of their shells, and the scratching also can help them shed. I had a turtle and he loved it so much I put a brush in his aquarium for him to rub up on

Some of them even do a cute little wiggle to get more shell scritches.

I had a turtle when I was a kid. Used to come up on his rock when I was near and stick out his neck, and rub the side of his head on my finger.

I didn't know they had nerves in their shell at the time, I was very little. But they do enjoy some scritches. So maybe?

I've never seen a turtle, but I understand what you mean.

i had one when i was a kid, and yes, she loved her shell being scratched. she would prop her back end under the entertainment stand and scratch away by rocking her back end side to side, funny to watch ill tell ya.