"Don't be afraid, I feel it too". Feel what?

But in this case, why is he so surprised that she resists him and even manages to read his mind? I had the impression that Kylo realized Rey was strong with the Force onlywhen she claims he's afraid of not being as strong as Vader, but maybe I got it wrong...?

The line is meant to be at first, "I'm going to be gentle with you" - it's meant to be contrast to how he could care less when it came to extracting the information from Poe. Versus trying to (initally) play Good Cop with Rey because of how she's a civillian, a young woman, and there's obviously a reason why he's immediately interested in her beyond wanting the map information (which having done cartography always struck me as the dumbest of reasons to think he could use her memory to create a viable map). Anyways, after TLJ came out, Rayne Roberts in that one SW Show episode admitted something we've long thought was the backstory here - it was Kasdan's idea and he wrote the scene. Ben initially tries to go easy into Rey's mind to extract that information because there's already a bond between the two of them. Both the Force and he senses that she's got the same abandonment/loneliness issues he has from her family. But once he tries it on her in earnest, it kick starts her abilities, she flips it back on him, goes into his mind, and in turn pulls out his deepest fear. Which forges the bond between the two of them, both the Force and the empathy/compassion. Snoke probably smells it on him immediately and figures he can exploit it to his own end (except duh, the emotional part is how he ends up dead).