Well, between Bach and Mendelssohn, baroque music had been out of fashion for a century. Mendelssohn revived interest in Bach's music. Doesn't mean Bach wasn't renowned in his own time.

Yes, that's a good point. It's hard to remember how long ago he was writing, until you think about stuff like the well tempered clavier, where being able to play in all keys on the same instrument is seen as a modern marvel. We are now so used to equal temperament that the compromised intervals sound normal to us, whilst they would have sounded wrong to them.

The major sub-periods of the Common Practice Period are roughly

* Baroque c. 1600–1750 – Pachelbel, Purcell, Albinoni, Telemann, Bach, Händel, Vivaldi

* Classical c. 1730–1820 – Haydn, Mozart, Salieri, Beethoven, Schubert, as well as Bach's sons C.P.E. Bach and J.C. Bach

* Romantic c. 1800–1910 – Strauss, Wagner, Chopin, Mendelssohn, Liszt, Dvořák, Tchaikowsky, Grieg, Sibelius

with quite a bit of overlap, of course – for example Beethoven and Schubert were both influential figures in the Classical–Romantic transition.