It is not too much to teach multiple things at once. Just keep the sessions short, to 5-10 minutes. We worked on sit, down, stay, come and leave it all in our first puppy class while housetraining and while he learned lots of other words like out, in, crate, up, etc.
Yes you can use a clicker as long as the dog knows that click=treat.
Yes you should go to class before your dog is housetrained! House training was covered in our puppy class. And bigger dogs are going to be trained sooner than smaller dogs. Puppies would have accidents all the time, mostly the combination of being on a leash and therefore not being able to go to the door AND the smell of the other dogs (especially in a place like Petsmart). Just be a responsible owner and ask where the paper towels are! Our trainer keeps the spray bottle and paper towels right on the front table!!
