Hello again tag,
I can explain some of this stuff.
All network services that listen for incoming connections need to use a well-known port so that other machines can find them. When you make an outgoing connection, it doesn't matter. You just pick a random port. But in order for someone else to find you, you need to listen on port 80 (for a web server) and your clients will look for your port 80.
Transmission works like this too. But it is software non grata so people want to shut it down. In response, it gets a little more clever by listening on random ports and then using its outgoing connection to tell clients what that port really is.
There is some magic and extra work involved to make that happen. That is where the "port check site" comes in. There must be some other server or servers that check your randomized server to see if it is working so they can tell other clients what port you are using.
Keep in mind that all of the above is assuming that your computer is directly connected to the internet. That is rare. In most cases, there is some intermediary between you and the open internet. That intermediary is usually your WiFi router. Some older DSL modems would use a different kind of connection and put you right out there, but you aren't likely to see those anymore. So, that "port" you are using actually has to be open on your WiFi router. Then your WiFi router need to relay messages back to your machine on that same port. The NAT-PMP or UPnP settings that Drew mentioned are what tries to make that work.
You mentioned that "Universal Plug n' Play Internet Exposure Test which said my equipment didn't respond, which is good news". That may not be good news. If you are trying to open a port for listening, you probably do want to have your equipment respond.
And to make things even more complicated, BitTorrent is a funky, but completely legal, networking protocol called UDP. So much of what I said about "listening" above doesn't even apply. Take another look at Drew's responses regarding http://www.canyouseeme.org/.
I just tried Transmission on Sierra and I can't see any difference. It runs fine. You probably don't have the same wireless router and ISP that I have though. Your results could be different. Maybe Sierra is not talking properly to your wireless router.
Can you tell us what wireless router you are using? It that what is making your internet connection too? Did you get it from your ISP? Any equipment your ISP gives you is junk. Mine is junk. Originally my WiFi was actually slower than my internet. I went out and bought a $30 wireless router, disabled the Wifi on my ISP device, and connected them in bridge mode. Now I get the correct speeds. My bit torrent works too. I suspect that is where your problem lies.