How to remove rusted screws?
What you have on the inside looks like a rusty nut on a rusty threaded stud that is part of the broken rusty outside handle.



You don't mention having tried a wrench (AKA spanner) - the closed end of a combination wrench offers the best grip. You may need to clean loose rust using a wire brush to get it to fit. An adjustable wrench might work better than the pliers you mentioned, Using a vise-grip (AKA locking pliers AKA mole-grip) on the outside may help if the outside parts rotate.



You could cut them off with a hacksaw, a rotary tool (Dremel etc) or a multitool.





Sometimes you can use heat to help free up rusted/siezed parts like that. If you have a blowtorch, you could try this. Personally I'd cut them off since you probably don't want to reuse the nuts or the outer handle..