I think that would look great!

Should be fine! Make sure that the two sizes match in color undertones before laying (try a dry lay first)

Often preferred as it is a separate space. Make sure your tile contractor can execute the pattern professionally.

That would work well!

We did that same thing because our laundry room is bitsy and we thought the smaller tiles looked better.

@barncatz would you happen to have a photo ?

I did that on purpose, too.

Same tile on the diagonal should look fine. Be sure to buy plenty. There can be a fair amount of waste with that application, but the visual effect is worth it. People at the store can help you figure quantity. We remodeled two bathrooms in the past couple years and had square floor tiles laid diagonally.