  We present the discovery of four low-mass ($M<0.6$ $M_\odot$) eclipsing
binary (EB) systems in the sub-Gyr old Praesepe open cluster using Kepler/K2
time-series photometry and Keck/HIRES spectroscopy. We present a new Gaussian
process eclipsing binary model, GP-EBOP, as well as a method of simultaneously
determining effective temperatures and distances for EBs. Three of the reported
systems (AD 3814, AD 2615 and AD 1508) are detached and double-lined, and
precise solutions are presented for the first two. We determine masses and
radii to 1-3% precision for AD 3814 and to 5-6% for AD 2615. Together with
effective temperatures determined to $\sim$50 K precision, we test the PARSEC
v1.2 and BHAC15 stellar evolution models. Our EB parameters are more consistent
with the PARSEC models, primarily because the BHAC15 temperature scale is
hotter than our data over the mid M-dwarf mass range probed. Both ADs 3814 and
2615, which have orbital periods of 6.0 and 11.6 days, are circularized but not
synchronized. This suggests that either synchronization proceeds more slowly in
fully convective stars than the theory of equilibrium tides predicts or
magnetic braking is currently playing a more important role than tidal forces
in the spin evolution of these binaries. The fourth system (AD 3116) comprises
a brown dwarf transiting a mid M-dwarf, which is the first such system
discovered in a sub-Gyr open cluster. Finally, these new discoveries increase
the number of characterized EBs in sub-Gyr open clusters by 20% (40%) below
$M<1.5$ $M_{\odot}$ ($M<0.6$ $M_{\odot}$).
