Gmail shows the time since an email was sent of received in the form of "7 Minutes Ago" or "1 Day Ago". However, this value remains until the next value has been reached. So for minutes it is simply just the next minute, but for hours it will be "1 hour ago" until 2 hours has been reached. Is it possible to get this feature to be more granular? If so, how?
You mean something like "1 hour, 37 minutes"? There's no way to get Gmail to do that. If you're good with userscripts you might be able to put something together to do that.
If you mouse over the relative time, you should get a tooltip to show the exact time.