You can. It adds a lot of work! It's surprisingly tough to sand. And sanding makes it look bad, so you end up having to use filler primer and/or bondo, then more sanding, and more painting. Here's an example: https://www.youtube.com/watch?v=ZTE9bJyUO_8
Yes, you can. If you want to do that, I'd recommend to print in ABS though. It's easier to sand and you can use vapor smoothing afterwards to get a very smooth and shiny surface.
Printing ABS is more challenging though and the fumes tend to smell.