How do monsters who do not use weapons fit into the expanded combat mechanics? Do you give their natural weapons, like claws, tags like regular weapons?
Yes, I would! Monsters do have damage dice for their attacks, so that translates in and of itself. Take, say, a lion:
5 HP, 12 STR, 12 DEX, 11 WIL, bite (d10), claws (d6+d6)
Now, a lion's bite isn't necessarily slow, but you could argue that it comes with more warning (I guess?). Either way, d10 attacks counting as slow is more balanced, in my opinion.
Beyond that, I find the idea of "Are the monster's teeth like daggers? Like swords? Talons like spears?" always translates quite well :)