I've enjoyed searching out a number of different Grease Productions and seeing how the music, scenery, choreography and role interpretations go. I've found a lot of them including both amateur and professional (some pretty good, others pretty bad--but still interesting).
Here are a couple of clips of a recent French production. One includes some rehearsing shots as well as make-up activities. I think Beauty School Dropout is sung in this one.
The other includes Greased Lightening and Hand Jive. Note how the songs are sung in a foeign language but some English phrases are retained.
Be sure you type in the entire URL to make them work.