I'm confused when большая means "large" and when it means "grand" - like here, it's apparently a "large" hotel, but in other cases, it's a "grand" theater.
As far as I understand 'Grand theatre' is a name. The original name was the imperial bolshoi theatre. Nowdays we call it Большой театр. When we talk about Grand hotel (Гранд отель) we usually mean luxury, very expensive and of course large hotel. The phrase Grand hotel isn't used very often in Russian.
I see the word guest "гость" in the word for hotel, is this just a coincidence or is hotel a combination of words?
As far as I know the -ица suffix roughly means "place of" so гоцтиница would mean "place of/for guests." I know for a fact this is the same in Armenian in the form of հյուրանոց:
A hostel can be translated as "общежитие or гостиница. Grand hotel you may only translate - гостиница. Sometimes гостиница is common name for a hotel, motel, hostel and even a guest house. And one more thing a hotel is often called Отель :)