You will get there, often it is starting off without a definite plan and adding ad-hoc Keep working on it.
However for your two paths. Too many screenshots so using imgur.
1) Taking a measurement from your path I estimate a diameter of 600 so I make a perfect circle that diameter and centered on the guides. This using the old shape-paths script-fu.
https://i.imgur.com/CrjUJo7.jpg
2) The Unified Transform Tool in Paths mode gives control points and a center rotation point that give an indication of how far off the center lines the path is. If you click-drag inside the tool you can move the path to suit. This I moved down and right to align with the (new) circle.
https://i.imgur.com/JmlRSDh.jpg
3) The semi-circle path needs a bit more attention. It needs moving up and it is not circular.
https://i.imgur.com/cg8PCeh.jpg
4) I can move up and align with the diameter guides but to deform to match the (new) circle I need to move just the top so hold the shift key down and drag down to fit.
https://i.imgur.com/iCemS77.jpg
5) Which gives result like this: ]https://i.imgur.com/C6PPko8.jpg
You do not have to keep it all circular, but it is preferable.
You can use the Unified Transform Tool with combinations of key modifiers ctrl / shift / alt which all give different actions and deform the NFT path to suit the non-circular semi-circle.