When an interface self-assigns an IP it generally means the interface isn't getting any response from your router or DHCP server. This is a feature of OS X to let the machines build an adhoc network when they cannot determine the actual network they're on -- you can put a bunch of Macs on a dumb hub and almost get them to self-organize and function with this feature.
Your router and DHCP server are going to see the MAC address listed for the device in the Network Preferences pane. Go to System Preferences -> Network and click on your Thunderbolt interface. Click on the Advanced... button and then on the Hardware tab:
That's the MAC address that your interface is broadcasting on the network when it's trying to acquire an IP on your network from your DHCP server.
The reason you are seeing the symptoms present when you connect an ethernet adapter to the TB port and not when you connect a monitor to the TB port has to do with what is being passed over the TB cable.
TB multiplexes at least 2 signals over the same connection. In this case, video and PCIe. Yes, basically the same PCIe bus that you would find looking inside any computer is now on that cable.
Thunderbolt Technology Brief
So, basically speaking, when you are connecting the DP to TB, you only get video. When you connect the ethernet adapter, you are connecting to PCIe. When you daisy chain devices, you get both.
Your mouse stops working because the ethernet adapter is generating noise that is interfering with your receiver. It is the PCIe "signals" that is creating this noise within the ethernet adapter. It is not interfering with the USB port - just the wireless radio reception/transmission of the receiver. I know this for a fact because:
1) I experienced it myself. I have a Logitech Anywhere MX (non bluetooth) and bought a TB to Ethernet adapter. I had the same issue. I changed out my TB to Ethernet adapter to a more reputable brand and the problem went away.
2) I found this answer on Logitech support forum
3) Plug in a USB hard drive. If it was interfering with the USB, the hard drive would fail as your mouse does.
The reason that when you move it from one port to another it "sorta" works is because you have lessened the wireless interference, not eliminated it.
Here is the Apple Ethernet adapter that I bought that solved my issue.
If you want to confirm this, buy a USB extension cable to move your unifying receiver to another location (sometimes logitech includes this with their mouse). Or, plug in the unifying receiver into a hub away from the ethernet adapter. The problem should go away.
Best Answer
I think there is something going on with El Capitan and a most recent update... My ethernet speeds (same network as an old Mac Mini) are 50x more (very seriously) than my iMac 5k. I get about 70Mb/s on the old Mac Mini and only about 1.5-2Mb/s on the iMac. I checked the network traffic, I checked the processing in the background ... nothing. That's changed recently (with nothing else changing) and I think it was due to an update. Frustrating though.