Semi-outdoor kitchen with metal studs
1) can the metal studs carry the weight of a countertop and the work that happens on there? They're designed to hold up walls after, which creates different forces.


Depending on the material of the countertop and it's span, sure. Metal studs should have no problem supporting a plywood with tile countertop. If your going to go with a stone (granite, marble, etc...) you may want additional cross bracing - again, depending on the span.


  2) how do I handle the drywall to be able to withstand being exposed to outside air? It won't be in direct rain or anything, but temperatures swing from 70-120 (20-50C) with high humidity.


Don't use drywall. Find concrete board or similar. Looks like drywall (in America, it's generally 3 ft x 5ft) and cover the concrete board with your material of choice - tile, some sort of vinyl material, etc... The concrete board will give the metal studs rigidity and stand up to weather better. This is how outdoor kitchens are built in NY where it snows and it stands up just fine.