Bridge from square to circle

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Hi all,
I am quite the beginner at Fusion 360 and I am looking to bridge a gap between a cilinder (so a circle edge) and a square. Below two screenshots to indicate the problem. My steps in sculpt mode:
- Convert the side edge of the cilinder. This results in a square around the edge. See the first screenshot.
- Convert the edge of the square (not shown)
- Bridge the cilinder edge (which is now a square) and the originally already square edge to form a cilinder/cone shaped bridge. Result shown in second screenshot
My questions:
- Why does F360 form a square around the circle when converting and is there a way to avoid this?
- The bridge is per definition a cilinder shape, but I (originally) have a square as one edge. Is there a way I can go from a cilinder to a square using the whole edges of both side? It may look a bit awkward but I don't see why this cannot work.
- The bridge never fully aligns with the edge of the cilinder (see second screenshot). I have used the match function on a different occasion to resolve this, but this does not lead to a smooth result. Is there another way to avoid this.
Would really appreciate your help. I am probably going to regret saying this, but please do not hesitate to give me direct feedback if you think it may help.
Thanks!
Richard