Feed vs. Activity Stream
Everything that you do inside your project is recorded so that you never miss an update. Feeds are a great way to keep everything in place. You add a work item, create a sprint, add or delete a user, push items across status - Every single activity is right there on your feed and you can know what's happening in your team.
Activity stream is similar to a feed, where you can track all the activities in your project. But, it is the place where all your activities are stored date-wise. If you want to fetch the activities on a particular date, just move on to the activity stream and get it in a few scrolls.
If it's a small team, you will prefer to have direct communication with your team. As the team grows, it is quite hard for the manager to focus on every single user and their work. This is where a Feed helps the team in knowing what's happening in the project.
What is notification?
It's always good to be on top of things and that's why you need a notification to be informed. You will receive notifications only for the projects and sprints that you have been added to.