Usually in a hostel one has their own room but may share a bathroom or kitchen with others. The general rule is that everything is tahir until you see it become najis, so assuming someone made something najis just because they don't know the tahara rules isn't correct. Let's say you do know some things become najis, it isn't wajib for you to make them tahir. You may keep your own pure utensils and also pure clothing for salah. As long as you keep a pure place for salah such as a rug and pure clothing then this is fine. One may also pray on a najis carpet apart from the sujud area provided that the najasa wouldn't transfer on them and remains dry.
May Allah grant you success