If Google indeed searches your emails on gmail.com for keywords to use in advertising, can they be trusted to keep your identity safe? What about tying your email and calendar to social networking - isn't there some danger in having a single account that ties a bunch of services together?
Google can be trusted as much as any large corporation. Once you view them that way then you can decide whether or not to use their products or services. They do offer some useful things, but will they respect your privacy over the long term?
Who knows? Even if they do so now, there's no guarantee that they will in the future once new management takes over the company.
No, they cannot. Google's goal has never been to protect your privacy, it has been to make money based on the fact that people respond well to being told what to buy when ads come up near your search query results.