Just as an FYI, new versions of chrome also sends back the full URL and the hash of any file you download or save. I bumped across this when I was trying to download light table and it din't let me open it. After a bit of research I found file scanning to be the new addition to chrome's malware checks. With all the NSA debacle going on now, I am feeling even more paranoid. I love chrome but I will be switching to Firefox or IE10 soon.
No, it doesn't. I've detailed how safe browsing works in Chrome, Firefox and Safari works before[1]. tl;dr only partial hashes are exchanged, so you can't reverse it even if you really wanted to.
Yes it does. Check this page out [1] and this stackoverflow question.[2]
"If a file isn’t from a known source, Chrome sends the URL and IP of the host and other meta data, such as the file’s hash and binary size, to Google."
Chrome is the most invasive piece of spyware you could ever install.
Unless you turn off some 10 or more options, it literally phones back your entire online activity, in or out of incognito mode, in or out of any google service.