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

The difference between Selection Tool and Direct Selection Tool: https://www.youtube.com/watch?v=CUPTflFXdjc

Convert stroke into path: Select “Outline Stroke” from the Path fly-out menu of the Object menu. Double-click on the Fill swatch to fill the path.

Background becomes transparent: use Cmd+Shift+D https://graphicdesign.stackexchange.com/questions/29661/illustrators-background-and-artboard-became-transparent

Draw a circle path and erase half of it (with an arc left):

Ignore certain layers when exporting: