Declaring Wharton in the UPenn application

Can you eg. apply to Wharton and say you’re definite you want to study finance and then apply to another school and say undecided?

By “another school” do you a different university or a different undergraduate school within UPenn? For the first case, you can freely put different preferred majors for different colleges you apply. In the second case, you would have to apply for a transfer to another undergraduate school within UPenn after you commence studying at Wharton. UPenn students in this group might be able to tell you more about the specific procedures for that.