However, as people say there is no such thing as a free l[STRIKE]a[/STRIKE]unch. Nobody shares a home with anybody for free. Therefore , I assume that a person has to pay his share of rent.
Am I wrong?.
Yes.
When a colleague of mine had some bad luck a few years ago I shared my rooms with him. As he paid nothing, we did not share the rent. Although people who share accommodation normally share the rent, this does not automatically happen.
Actually, 'share' in these sentences is not always clear. I can say, for example, "My friend and I have separate flats (apartments) on the ground floor of a small house. We share the house with three other tenants." There is no agreement, financial or otherwise, between my friend and me or between either of us and the three other tenants.
My comments on your original questions:
''He needs a roommate to split the cost of rent with''.
That is clear.
''He is looking for someone to share accommodation with''.
Fine. The assumption is that they will be splitting the rent, but this is not explicitly stated
''He is looking for a roommate to share rental cost with''. OK,
though I would say "The rent" rather than "the rental cost".
Unlike billmcd, I prefer the "with".