The default theme (and some other themes, I think) makes the thumbs square. Is there a way of displaying a square placement for the thumbs, then let the vertical/horizontal thumbs be placed within those squares, without any cropping? Many thanks.

Yes, uncheck the crop option on the admin options. To get a uncropped image to fit within widht x height you need to change your theme to use the quite new maxspace functions. Please try a forum search on that.

This is exactly what I want to do (uncropped thumbnails).

I looked through the options and I don't see a "crop option on the admin options" that I could uncheck. Can you give me some pointers?

That option is listed under Options -> Theme.

The mentioned "maxspace" functions need to be implemented directly on the theme files and you need to replace the existing image function calls with them. The "maxspace" functions do use the admin backend options therefore does not matter if cropping is set or not to get them to work.