Clear forest / improvement before building?
This is a rather subjective question, and the "correct" answer will vary according to game situation. It all depends on your priority.
I will say that I typically do not remove forrest by putting a district on top of it. Instead, I will produce something else, and chop the forrest to help produce it faster. When I have finished that thing, I will then start the district on the tile that previously had a forrest.