What free video editing software is capable of moving/rotating a sprite atop video?
A great tool for this is Davinci Resolve: https://www.blackmagicdesign.com/products/davinciresolve. It is very capable, has an excellent free version and can easily accomplish the desired tasks.

A quick intro to Animating a Spite/Image over Video is shown here:  
                
             -- Davinci Resolve - How to Move Images (Animate Movement)

A quick intro to Masking can be seen here: 
                
             -- Masks in DaVinci Resolve 16