I plan to be in the Tanglewood area July 8-11. If there any performance going on at that time, even not on the main stage?

Yes there is. Check their website for info and tickets

Yes check their website July is a busy season and could be sold out for whatever you want to see unless you buy in advance. The previous weekend I'm seeing James Taylor

July 8 at 2:30pm boston symphony - Brahms piano concerto No.1 and Shostakovich symphony No.5 July 11 8pm Prokofiev Visions fugitives, Beethoven Sonata No 30 in 3 Op. 109 and Schumann Fantasy in C Op. 17 Hope that helps!