1. I would recommend you to use qBitTorrent since it's open source and doesn't have ads.
I preferred that one as well, but I keep getting inconsistent results [not sure why] with zero inbound connections:- Bitnode = Unreachable
- Other port checking websites = Open/success
2. Can you download/upload something on uTorrent when Bitcoin Core has incoming connection?
Yes, there's no issue with doing those at the same time: Screenshot
I forgot if UPnP is turned on by default, and I'm assuming the torrent client uses it to open the port. Can you go to Settings>Options>Network and check Map port using UPnP?
It wasn't turned on by default, but that did the trick [thank you so much] 
- Can someone merit his/her post on my behalf (I have no sMerits).
I'll lock the thread in 24 Hrs.