Do images need to be resized before adding, or will they adjust themselves to fit?
You have to adjust them before. Tiles can't automacally adjust them because we don't know the width in your page. With one of the next version there will be the option to resize them to a given size automatically.
How do I remove unused tiles from a Gallery?
You just delete the position and save the tile. A real delete is not designated, because you can easily reuse them or store them for later.
Do the galleries have to be placed as a module or can a short code be used within an article?
Normally just as a module, but you can if you want have modules in arcticles (;
docs.joomla.org/How_do_you_put_a_module_inside_an_article%3F
Best regards
Yves