It is a computer, but the question is do you want it to show media or research rocket science?

Yes, simply install a third party launcher. Connect keyboard and mouse either via USB or bluetooth will be better.

Yes

Yes, you can either sideload Android apps or flash the full version of Android to the device.

Compatibility and power will obviously vary.

I've been doing this for a while.

I'm using Android 9.0, not Android TV OS.

It works fine for a browser (Chrome) and I use it for that often. In theory it will work fine for email, but since I always have my cellphone with me I haven't really tested that.

Facebook ap works. So does messenger, but I turned that off as the notifications were popping up while I was watching movies and it was distracting.

I don't use it for music much. Youtube works fine, but for music it uses the TVs speakers and I've got a better set of speakers for music. So I've only really used it for music when I want to watch the video.

Basically it will have the full functionality of a cellphone, minus the camera, GPS and microphone (although you could hook up a USB Camera and get the camera/microphone functionality, I've been thing of testing that with an old webcam I have lying around and Skype on the box).

I loaded WhatsApp messenger on it once. It worked, but WhatsApp only works on one device, so I soon migrated it back to my cellphone. I haven't tried Instagram or Snapchat, but Snapchat might have trouble with the lack of a camera. Twitter works fine.

I haven't tested any of the MS Office apps on it yet. In theory they will work fine, but I would imagine that it will be slow, the office apps use a lot of overhead, and most of these devices have pretty underwhelming processors.

It links to my fileshare server, so I have access to all my files without worrying about running out of memory.

The only required hardware is a USB wireless keyboard/mouse combo. In theory you can use just a wireless mouse and the onscreen keyboard, but I don't like the onscreen keyboard. A real keyboard is much more efficient.

Is it possible to browse the web, read & write e-mails, play music/videos, write documents with a mouse and keyboard?

Technically, yes. You can attach a mouse and keyboard and use a browser app to access web based email or use Google Docs. If that's all you use a computer for, then an Android TV device can act as a computer for you. Basically just look at these devices as a smartphone/tablet that doesn't come with a screen, so you have to attach it to an HDTV. If you can do it on a phone, then you can pretty much do it on an Android TV device.

https://play.google.com/store/apps/details?id=io.appground.blek

for your mouse/keyboard issues

There are ROM’s available like the Lineage OS that has pretty good support for desktop type Android work, BUT when using such ROM’s you loose WideVine L1 DRM and HDCP - that are essential for copy protected 1080p and 4K video streaming from Netflix, Amazon Prime, HBO Apps etc..
https://lineageos.org

The other problem is most Android TV devices are impossible to Root to install such ROM’s and most of the cheap ones use slow underpowered chipsets for demanding desktop type work.
A cheap Chromebook would be a MUCH better solution.