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Where does he place in terms of skill and strength in the MCU?

He has 0 skill in his own universe. He's just the physically largest and strongest human in Westeros and has armor that's mostly impenetrable.

He's not probably around Peak Human-Class 1. As nothing he did is even close to someone with legit comic suoer strength.

Well he's stronger than Hawk Eye lol.

Zombie Mountain is a lot stronger and tougher than a normal human. That's pretty much undeniable. But he is also extremely slow and has virtually no skill to speak of. Without prior knowledge, some people might get caught out by his damage soak, delivering a blow they believe fatal only to be caught off guard when he is still alive. But if they know about his damage soak and have a weapon that could decap him, I could see him losing to most skilled swordsmen.

Mountain didn't even fully crush Qyburns head against the wall. It wasnt until he smacked against that rock after he got thrown that his skull split open.

And as durable as he is, that's not too impressive in a decent comic world like Marvel or DC.

Like Vault pointed out, unless someone just doesnt know he's super tough and they dont make sure he's finished off he could catch them by surprise if they're not paying attention. But he doesnt beat a single swordsman or fighter of note.