Is it possible to get font size in any apps in OS X? I want to get font size (and font family, if possible) that is used in any Mac applications. For example, in Calendar.app, you can find that the date is bold and bigger than any texts that is displayed on the app. 

Is is possible to investigate the font in any texts in any applications in OS X? Or is there any app like the Chrome extension WhatFont, (which displays the font information including size and family under the cursor)?
WhatFont is not as magical as it seems - it's simply surfacing information already present in the web page coding (the font being used) in a way that is easy for non-technical users. There is no program that I am aware of that will identify fonts under the cursor when the information is not already available.

MyFonts has a service called WhatTheFont! where you can submit a screenshot and it will try to identify by matching your image against known samples in their database.