a number of games, which likely rely on google services.
For ads, mostly. The vew i tried, one didn't let you select start because of a bug with a missing ad frame (imagine!). The 4 or 5 others ran fine. Might look different with the 90% of games who want to rip ypu off. Payment ingame might rely on Google Services too.
Yes, but like @kuneho said, since "deleted" stuff only is marked as deleted (not wiped), there's always a bunch of random on the "empty" space part of a disk, which compresses badly.
Do cat /dev/zero > /path/to/mounted/partition/zeroes and delete it after cat errored out because no space, to fill the "empty" space with zeroes.
No, i wouldn't normally visit any site with the advertising and tracking.
At least they mention that they track you. Most talk only about ads.