Hi,
I still say that the only reason Claire is going out with you is because/that she feels sorry for you!
Will you use because or that in the above situation? Say 'that'. If you search the Forum with 'reason because', you'll find quite a lot of discussion on this point.
Moreover, is it the same as the part in bold in meaning to say the following?
she feels sympathy/compassion for you Yes, broadly speaking. But these words are more formal.
she feels sympathetic/compassionate about you Yes, but it's better to say 'towards you'.
Best wishes, Clive