Is it correct if I say I went up the steps (for inside a house) instead of saying I went up the stairs?
If it is not a full set of stairs, but just a few steps, I'd use 'steps'.
The steps on this set of stairs are very narrow.
The stairs leading up into the tower are very steep.
Each step of the staircase is covered with carpet.
Please take a look at this photo.
What is this man doing?
- He is climbing the stairs two steps at a time. [Is this correct?]
The set of steps depicted is not inside the house/building, leading from one floor to an upper floor - hence, not stairs.
He is climbing a set of steps/he is climbing the steps, three at a time.
I think this is correct, why?
I'm guessing that stairs is often refers to a set of steps as in a staircase and there is not just one and for refering to only one of those stairs we say A step? and also when we have just a few steps we usually say steps and not stairs. Is this correct?
Yes, though it doesn't have to be singular- you have two and three steps used in the earlier posts in this thread.