When someone uses the term mid-length they're talking about the entire gas system. There is a little hole (called a gas port) drilled in the top of the barrel that lets gas into the gas block, that lets gas into the gas tube, that pushes on the gas key, which is part of the Bolt Carrier Group, whose movement backwards unlocks the bolt, extracts the spent case and then ejects it out the ejection port.

The gas port must be at an appropriate distance down the barrel to use it's corresponding gas tube. Carbine port->carbine tube, mid-length port->mid-length tube, rifle port->rifle tube. Otherwise you're going to have a bad time. Or at least a very boring time.

When this other forum post referenced "carbine barrel" they were probably talking about overall barrel length. 14.5, 16, 18, and 20 inches being popular AR barrel lengths (16 being the minimum allowable without running afoul of the NFA). The 20 inch is the original design and uses a "rifle length" gas system. The 14.5 is the current M4 design and uses a "carbine length" gas system. For 16 and 18 length barrels you have more options and in those cases, yes, a mid-length gas system CAN have an effect on recoil (more space for the gas to expand into means less impulse on the BCG)

And, yes that handguard does say it comes with a barrel nut. Personally I despise Cheaper Than Dirt and NcStar does not have the best quality reputation, but it'll probably get the job done. Note that that handguard says it's "designed for a carbine length gas system" so if you did go the mid-length route, you'd have gas tube sticking out in front of your handguard.

Something like this barrel nut/delta ring assembly along with a handguard cap placed behind your gas block (make sure you get a handguard cap of the proper diameter for your barrel) would allow you to use the previously linked handguard and many others.

Honestly, all of this is why many people purchase their first upper pre-assembled.

Hope this helps.