cudatext as a notepad replacement. It's closer to a full featured text editor, but is very quick to startup with no extensions installed.

I have no idea about replacing paint, but irfanview for simple viewing, cropping, resizing, swapping formats, etc.

For calculator stuff I sometimes just open the Python REPL. If you know the language (even a little bit) it does all the things and more. Every time I try to use the Windows calculator it annoys me trying to find the right button and them accidently putting another operator instead of equal or vice versa.