As @bmike said, Internet Sharing hides a lot of complexity behind a very simple interface, and some of your questions can't be answered authoritatively without interviewing some of the Apple engineers behind it. But that won't stop me from taking a stab at it...
1) AirPort is different from the other interface types because in order to share over AirPort, your Mac has to actually create the wireless network (as opposed to just providing service over an existing ethernet, FireWire, etc connection). This means that InternetSharing needs to have a bunch of info about how to create the wireless network: network name (SSID), channel, security, etc.
2) Resharing over the same ethernet interface is useful under some circumstances. For example, on my home network my ISP provides limited number of static IP addresses for my use. I run a Mac doing the equivalent of Internet Sharing (actually, I set up the daemons manually as @Spiff recommended) to reshare over the same ethernet. Result: if I put a computer on my home ethernet and config it via DHCP, I get a private (behind-the-firewall) IP address from my virtually unlimited internal pool. If I manually config the computer with one of the public IPs, I get full unfitered internet access, but use up one of my limited public IP pool. Because they're both on the same network, "moving" a computer behind or in front of the firewall is just a simple configuration switch.
On the other hand, if you did this same trick on an ethernet network that already had a DHCP server, computers attaching to the network would randomly get configuration from one server or the other, leading to unpredictability, confusion, and hair-pulling. It's definitely a use-only-if-you-know-what-you're-doing feature. Fortunately, Internet Sharing is smart: if it detects another DHCP server on "its" private network, it shuts itself off to avoid trouble.
3) I don't know of a way to change the private IP range on an IS-created wireless network. On the other hand, it shouldn't really matter, since the network is being created by Internet Sharing, and therefore it doesn't have to worry about conflicts with any existing network numbering.
4) You can add interfaces with Apple's USB Ethernet Adapter. Get some USB hubs, and pile them on!
This depends a lot on your DHCP server, but I would look into using the client id to assign static IPs. It's not tied to the individual hardware (although you'd have to set it at least once when they first use a TB Display), so it avoids the switching displays problem. It can be set via the networksetup tool.
Best Answer
When there are 2 routes available, I usually just temporarily Turn Airport Off in Network Preferences when I want to force a transfer (or other network connection) to start over the wired ethernet port.