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Crop out paths outside artboard: https://graphicdesign.stackexchange.com/questions/40917/how-can-i-crop-everything-outside-of-an-art-board-in-illustrator
Any other way beside using pen or brush tool to draw a path?:
1. refer to the official list: https://helpx.adobe.com/illustrator/using/drawing-simple-lines-shapes.html
2. maybe pathfinder > compound & shape builder tool: https://youtu.be/aGFWmYHUQOU
Draw a circle path and erase half of it (with an arc left):
The difference between Selection Tool and Direct Selection Tool: https://www.youtube.com/watch?v=CUPTflFXdjc