If its a terrace with out a top is it still illegal to bbq on it?

Answer 1

It will be hard to answer you correctly without know a lot more of where you are talking.
Since this is in renting I have to assume you are asking if it is legal to BBQ at your place. You will have to look at your lease and see if there is anything in it that would stop you.

Someting you might try is an electric BBQ grill. It was OK because there was no real fire.