GIMP Version: 2.8.14
Operating System: Windows
OS Version: Windows 7
GIMP Experience: New User

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I am trying to rotate an image about 10°. When I do part of the image gets cut off. How do I fix that?

... See Nidhogg's post

Ella Louise, don't make things too complex if you don't have to.
Rotate first, then use: Image/Fit canvas to layers. Just below the Canvas size...

I have a new problem. It is printing the wrong size of image and from the wrong paper tray.

If you print straight from Gimp, click the general tab, select your printer from the list and use preferences to select the tray you want to use and to adjust other printing settings.
These are device dependent setting so you need to figure it out yourself.
The size is not "wrong", it's probably just too small image you are working with?
Don't expect anything with thumbnails or regular web images. Your raster image better be of higher resolution if you want to fill A4.
Could be a good idea to use A4 (300ppi) as a base layer for printing if you are printing A4 size. You get it from File/New/Templates.

Sorry Nidhogg "There is more than one way to skin a cat."
But because you find it too complex, I'll remove my explanation...

There's no need to apologize for such thing Ella Louise,
I think removing your explanation was also unnecessary even if my was easier.
Have a nice weekend and please don't skin meeeeee! *meow*

Sorry Nidhogg, that does not seem to be the problem. The image is getting resized for letter (I live in the US) despite the measured print size being 13"x9". I have ledger (comparable to A3) paper in my printer's second tray. The print quality is fine. The image is not blurry or pixilated.

I don't think you can skin a wooden avatar, Nidhogg Have a nice weekend too.