How to choose Chrome extensions with security in mind

Is there a way to install an extension without actually granting everything it wants?

Only for optional permissions, but "Read and change all information on all websites you visit" is usually required.

Is there a database of trusted extensions that underwent rigorous auditing? Other ways to identify them?

No, at least none that are advertised by Google.

Any specific protocol I should follow when choosing and installing an extension to ensure security?

"Read and change all information on all websites you visit" is actually common. If it requires other permissions, such as "Capture content of your screen", then you should be more worried. There are some more here: https://developer.chrome.com/apps/permission_warnings

Make sure that the permissions make sense for the extension. Reading all website data probably doesn't make sense for a new tab page. Reading the code is always best.

Are there extensions that are endorsed by Google and have their seal of approval? How to identify them?

Some extensions are published by Google. Those are the only ones they endorse.