all pokemon have their ability, they can be given a number of items with interesting properties, but held items will be rare ( I mean seriously why can't I put amulet coin (an amulet) and mystic water (a necklace) on the same pokemon? as for moves the whole 4 moves thing is part of the sport. pokemon know all their moves up to their level (I won't be enforcing a strict level, but have a sort of range you want to work within. pokemon grow and learn more as they go just like people). If you get into any "official" battles you will be asked to select 4 moves for that fight, and one held item. This will be if the group stumbles upon a tournament or something or even just wants to end a dispute with an official battle.

For type matching I've always seen it as it's not just the material but the elemental powers there. that rock throw is infused with the element of rock. if a human just threw a single stone then it'd just be normal type. If a human caused a rockslide then I'd let that go up to a rock type attack. It has a lot of context sensitive parts. a fire type can drink water, but if you splash a whole bucket of water on them it'd sting, a fire hose would hurt like hell.

as for mega punch vs mach punch I'd say thats because mach punch is a fighting specific technique while mega punch is just a really solid punch. anyone can learn to punch hard it's very hard to master mach punch.