1. With Paint, which I have, I know how to enclose a section of a picture with a rectangle or something, but what do I do to simply create a new image from just this part of it?
I think with Paint you have to use Image>Attributes and alter the numbers to change width (from the right) and height (from the bottom). To trim the top or left you have to rotate/flip the image. Well that's what I do anyway, it's a bit fiddly.
3. Is there any other freeware I should investigate?
Yes, well if you have a digital camera you might have some very useful software with it.
I have a Kodak camera and the Kodak software is useful. You can import a jpeg and do the trim action as above but in one go by drawing a rectangle and adjusting it (like you want to do).
It also allows quicker adjustments of contrast and brightness.
The Kodak software also provides additional printing options e.g. you can create a business card from any image: just select to print eight small-size images on an A4 sheet (250g card) and then use a guillotine to cut them up.
John W