Removing a light switch cuts power to my entire room. Breaker not tripped. Smart Switch Install
Because of what you did with the neutrals

You needed a neutral so you unbundled one from that bunch of "spare neutrals back there".  That's what broke it.  It is a common misconception. 

All those neutrals already had a job to do.  Since you have seen the results of disconnecting them, you know what that job is.  I bet if you plug a 3-light tester into the downline sockets, you'd get only 1 yellow on the end. 

Anyway, reconnect all those neutrals the way you found them. This should restore your plugs.   I understand your smart switch needs a neutral, you need to add it to all those neutrals.  If it binds 3 neutrals it will now bind 4. 

Not all whites are neutral.  All neutrals are white, but not the other way 'round. Wire color does not designate function, but is simply how cables are made. 

Now there are two other potential problems.  


That brand is not sold by any reputable shop.  It is sold only on Amazon "Marketplace" and eBay (and Walmart which simply relabels Amazon listings).  That almost certainly means the brand is a Chinese cheapie that is sold that way to evade product safety laws. It cannot be sold retail because is unable to qualify for a UL listing (or equivalent Nationally Recognized Testing Lab), becuase it is unsafe. You should never install products like this, and you will face severe civil liability if there's fire or injury as a result.  The sick thing is, they're not even that much cheaper than listed product. 
it sounds like you are renting. You must never do any electrical work without the permission of the landlord.  Even with permission, electrical work in a rental unit must be done by a licensed electrician, though your local jurisdiction may allow self-changes of receptacles and light switches because they are pretty simple.