There are different types of MIMO. Those are Precoding, Spatial multiplexing, and Diversity Coding.
Precoding
The idea behind MIMO is that at the frequencies being used, the wavelength is small enough that even 30 cm apart is enough to receive the signal at different phases. As Brain said, the wavelength is about 12.5cm for 2.4 GHz. This means that regardless of how far you are from the two antennas, the delay (or phase delay) between the two antennas will always be fixed for any given angle.
You are able to take advantage of this phase difference to create beam steering. The math and actual implementation of this is complex, but the general idea is actually relatively simple. If the two signals are in phase, then you know that the source of that signal is the same distance from each antenna which means that your source has to be somewhere along the line of symmetry.
As the source begins to move around, the signal will get to one or the other antennas first and the angle from the receiver can be determined based off of the amount of delay between the two. This then allows you to setup "sectors" or beams based of off how much delay is applied to the incoming signal.
Now technically the drawing I showed is only MISO (Multi in single out), but the logic holds true when you add another antenna to create a full MIMO. Also, on the transmitting side, you can do the same thing I talked about with receiving, but instead a delay is applied to one or the other antenna to create a beam in specific direction out of the transmitter.
The accuracy of the angle in and out of each pair of antennas is determined by both the spacing of the antenna and the accuracy of electronics to produce and detect a specific phase shift.
Also things get more complex as you start to account for the fact that at some locations the signal might appear to get to the antennas at the same time but are actually 1 full cycle apart. Also there has to be a control system setup to know what direction you should be directing you beam at, especially when you have a moving device.
But to get to your question directly, it doesn't matter if your source has 2 antennas or not, it is treated the same on the receiving end. What maters is the angle that the source is from the destination. You essentially end up with a source directing its beam in the general direction of the receiver and then the receiver is steering its beam in the general direction of the transmitter.
The big advantage of using MIMO is that you are not creating a lot of extra noise for neighboring devices and so you are able to get more devices in to a small area. Also, since the signal is more directional there is less to bounce off of which results in less issues with multipath.
Yes. The 802.11 Medium Access Control, which is in charge of deciding on the data rate between two WiFi devices (which use IEEE 802.11), scales the data rate between the devices depending on a lot of things. One of them is signal strength. This correlation isn't necessarily linear, but it can be. Some packets are transmitted at 1Mbps while data is typically at the max speed. When the signal is not stable, it's common for the data rate to vary quickly. For more information see 802.11 Wireless Networks: The Definitive Guide, Second Edition
Best Answer
First, a 125 kHz square wave signal contains significant energy in higher harmonics, e.g. 1/3 the amplitude (a) of the fundamental frequency (f) at 3 times f, a/5 at 5*f, a/7 at 7*f... This means that the output coil is radiating at multiple frequencies, at least in to the AM broadcast band for a moderate quality waveform.
The wavelength of 125 kHz is (3 * 108 m/s) / (1.25 * 105 s-1), ~2,400 m (2.4 km). A quarter-wavelength is the "standard" moderately efficient antenna, so you could use 600 m long wires on the transmitter and receiver to increase range. That would be impractical for a classroom experiment, though.
You have some other ways to increase the range though:
You can combine a parallel-tuned "tank" circuit with a base loaded antenna and greatly increase range.