In miniseries "Strauss Family", Johann played violin as well as piano

No, Mozart's Violin Sonata in F Major is a secular classical piece, as is most instrumental classical music.

No, Wolfgang Amadeus Mozart was not a dancer. He was a musical prodigy who played piano and composed classical music for piano, violin, and other instruments.

He wrote piano music, solo (with piano accompaniment) pieces for violin and cello. He wrote pieces with orchestral accompaniment for piano, violin, and cello. He wrote chamber music for string quartet and for piano trio (piano, violin and cello). Most of his music is orchestral and operas.

No. Beethoven wrote music in every classical genre, solo piano, chamber music, symphonies, solo songs, an opera, choral works, overtures, and concertos for piano, violin, and piano trio.