Can I cast sorceries in combat phase, or only instants? For example, could I cast Press into service after blockers are declared to take control of a declared blocker?
You may only cast sorceries when it is your turn, during one of your main phases, while the stack is empty. So no you cannot cast them during combat.
307.1. A player who has priority may cast a sorcery card from his or her hand during a main phase of his or her turn when the stack is empty. Casting a sorcery as a spell uses the stack.