Chrome happily installs from an OS X standard account, it does not need to be installed by an administrator. As such, it probably isn't able to put stuff "everywhere".
BTW, maybe it's just me, but I have installed Chrome as its own user. That makes it more difficult for it to spy on my day-to-day activity.
~/Library/Application Support/Google/Chrome/
~/Library/Google/GoogleSoftwareUpdate/
~/Library/Google/Google Chrome Brand.plist
~/Library/LaunchAgents/com.google.keystone.agent.plist
~/Library/Caches/Google
~/Library/Preferences/com.google.Chrome.plist
~/Library/Preferences/com.google.Keystone.Agent.plist
Nowhere outrageously surprising, really.2) Frankly, Google is far more trustworthy than almost any randomly selected software company. (Don't forget that there are far more software companies out there than either of us are aware of.)
3) Unless you've taken the time to configure a MAC system, software that runs as you can access any data and transport mechanism that you can access. That's a fact of life. Anything you run on your computers can also act as a little snitch.
2) I sort of agree with this. Google certainly don't want to sell my keystrokes on the black market. However, they do want to store them and learn more about me and my personal autonomy and privacy mean that I don't want them to have all my data.
3) Which is exactly why one should be careful what software one installs!