typography

Personally, I would not recommend utilizing a service like that as it is a little concerning linking all external links via it. However, there are numerous areas where you can add in Javascript if you wish, such as the Analytics integration. This will add any Javascript to the header of the community on each page load.
This one is outside our scope of support but you can also modify your globalTemplate in your theme to include this script where you would like. For more on themes, go to: 
 

I don’t think that is possible. 
That part is easy. Just open the front end block manager as admin and remove it. 

One work-around could be to set your Thanks reaction so that it doesn't add a positive score to reputation. You'd still have the reputation in place but at least it would stay at zero for all people. Another is to bear in mind that on 4.6, the reputation score doesn't show in the author pane when viewing a topic, and with a quick CSS edit, you could hide the reputation entry which is shown when viewing a profile. If you did that, then it wouldn't matter that the reputation score is increasing, since nobody would get to see it anyway.

Front-end...

Hello,
Adding this to your custom.css file will add a scrollbar and restrict the height of your code box.
.ipsCode{ max-height: 400px; overflow-y: auto; }  

No typo - I am seeking to confirm when you can generate the error. Your last post there goes against this statement now:
Are you now saying that you DO get an error when "Ignore Topics" is disabled?
OK - seen your edit now might confirm my suspicion.

@Nathan ExplosionClose and it may have been a typo on your end, but this is it:
"Ignore Topics" DISABLED "(NE) Hide Content" enabled - Correct No settings applied in "(NE) Hide Content" (as per your provided screenshots) - Correct Result: the error you are seeing is gone now - Correct

Yes, I do have Adriano's 'Ignore Topics app installed. I have disabled IGNORE TOPICS and activated your APP and no error is generated. 
 

There is a plugin 
but it isn't available for purchase and it wasn't updated. I've messaged author some time ago but no reply so far.
Maybe someone would create a new version?
 

First, better as a separate mod, but easy to do.
Second, fits with KS, probably doable. You may wish to make a note in your terms of service or privacy note though about this that mods can see anon signed in users.

A couple of other requests if possible:
-The ability to download and export their private messages
-The ability for moderators to see users logged in anonymously in the 'Who's Online'
-

It is default IPS Editor functionality, so maybe. If it isn't working as shown above then log a support ticket.

Will answer my own question....this can be found unders Members---->Groups---->Usergroup you want to make the change in.

Already done. Will be in the next update.

I think there is a way. You can set up a new storage settings an use this as storage for download files.

Yes, absolutely it can.  
IPS supports Amazon Web Services (AWS) for storage and delivery.  Keep in mind that you will incur incidental costs for storage, bandwidth, and potentially CDN delivery.  
Guide:  https://invisioncommunity.com/4guides/advanced-options/server-management/configuring-amazon-s3-r230/