Important Points

Security
Always make sure you are downloading the crx file from correct source only, since the code is available publicly, anyone can put some malicious code in it and create the crx file and distribute it.
Extensions are very powerful and one of the possibilities is that all of your passwords can be stolen by a malicious extension.

---

Permissions required by Extension

1. Read and modify your data on moodle.niituniversity.in : self explanatory.
2. Read your browsing history : This is triggered by permission "tabs". This permission is needed to open a link in a new tab which the user clicks inside the extension.It is weird that "tabs" pops up this kind of permission, maybe because before opening a new tab chrome checks where a similar link is already open or not, thus requiring browsing history permission.

If you see any permission other than those mentioned here, then you are probably downloading a wrong(and possibly malicious extension)

For more details click here.

---

Why I am not seeing a notification for a new file even though professor added it recently ?
Because the course structure rarely changes, the course instructors mostly upload the files once and just hide it for next session and then unhide it at appropriate time, for this type of activity no notification is triggered by moodle.

---

So What kind of notification can I see as of now ?
Whenever the course instructor post anything on the forum, creates a assignment where you are supposed to submit something through moodle and if any file is uploaded(not unhidden) on the moodle.