Can users get notifications through the normal native popup notification on the forum rather than by email only? If not is there a plugin for it? Thanks!

You setup the defaults in the ACP as well as what options members have for each type of notification.

Search notifications in the ACP quick search. 

https://invisioncommunity.com/notifications/options/

Choosing one of those "Notification list" options and unchecking email would do what you want to do at a user level, and as Morrigan pointed out, you can also set the defaults up (including which options are available to users) in the AdminCP.