room/seat/place

  1. Is there room for me in the bus?
  2. Is there seat for me in the bus?
  3. Is there place for me in the bus?
    Are these sentences OK and are synonymous?

Is there a seat for me in the bus.
Is there a place for me in the bus.

Only ‘room’ is uncountable here. The others need the article.
They would usually be synonymous, but it is possible that ‘Is there room for me…’ is not. For example, if a man is trying to get on the bus with a bicycle and two suitcases, he might require more space than a single seat or place. In such a case, ‘Is there room for me…’ is not synonymous with the other two.