A
Please suggest the best 1 tb external drive (non powered). I will connect it to my wifi routerand use it for cloud storage.
Suggest external drive
1 TB external hdds aren't VFM. 2TB is the way to go. And unless both your router and receiver devices use the AC wifi standard (for lan) and router's usb port is at least 3.0, your makeshift cloud storage will be slow.
A
Yes it's 3.0. I have the netgear nighthawk R7000. Suggest a good 2TB then 
W
WD my passport or seagate backup plus slim,pick whichever brand you had good experience with in the past.
I personally use WD My Passport 2TB, have 2 more at my home. It doesn't look good but does its job fine. Get a casing for it.
B
Is a casing really helpful in case of drops?
FYI, In my case, usb 2 was sufficient. Streaming 6GB over AC wifi, downloading @ 10MB/s with no issues. Of course different needs, different speeds
W
All depends on your luck but I wouldn't recommend to trust a dropped hdd no matter what case it was in.
Depends, but generally, yes. It's better to fall with 2 sponges attached than w/o them.