Notes on iPad Pro 2020

Hello all. Let me just start by saying I'm a 30 yr old SAHM who's going back to college and NOT tech savvy at all! So please excuse my question if it seems simple to you and when you answer my question, please answer in the most simple terms possible! lol

I currently have a MacBook Pro 2019 A1990 15 inch (which I still don't know how to fully use) and I'm looking to get the iPad Pro for college next month. I don't want to use my laptop because I'm not good at typing my notes. I'm more of a pencil and paper kind of girl so I saw that the iPad Pro you can write directly on the screen.

My question is, with the apple pen, can I write directly on the screen to take notes on the iPad Pro? or for example, in math class, if I want to write out my work or a problem, can I do that in the iPad and save it someway? Basically I'm asking if I can use it the same as paper and pen and if so, will it save my actual writing or will my words turn to a typed text? for whoever takes the time to read this and answer, thank you!