In Windows Explorer, one can view folder contents' details such as size and number of files on mouse hover. Is that also possible in Nautilus? In other words, how can I trigger Nautilus, if possible, to display a tool tip or notification box of some sort on mouse over a folder or directory?
SnapOverflow
Neither Thunar, PCManFM, nor Nautilus have this feature, I don't know about Dolphin as I don't have it Installed, while I think is possible they could have it they don't currently use it.
As @Tom mentioned in the comments, Gnome Sushi is the closest to have that but you need to press the Space bar for the window to show and I don't know if if it's a bug only affecting me but the Sushi window uses a Black background with black text making it useless but you can still try it.
No, as I know, there is no such a method. But you can right click -> go to Preferences.
There you can look how many files are in the folder, how big they are etc.