Joint Radar and Communications (JRC) can implement two Radio Frequency (RF) functions using a single of resources, providing significant hardware, power and spectrum savings for wireless systems requiring both functions. Frequency-Hopping (FH) MIMO radar is a popular candidate for JRC because the achieved communication symbol rate can greatly exceed the radar pulse repetition frequency. However, practical transceiver imperfections can cause many existing theoretical designs to fail. In this work, we reveal for the first time the non-trivial impact of hardware imperfections on FH-MIMO JRC and model the impact analytically. We also design new waveforms and correspondingly develop a low-complexity algorithm to jointly estimate the hardware imperfections of unsynchronized receiver. In addition, using low-cost software-defined radios and Commercial Off-The-Shelf (COTS) products, we build the first FH-MIMO JRC experimental platform with simultaneous over-the-air radar and communication validation. Confirmed by simulation and experimental results, the proposed designs achieve high performance for both radar and communications.