We report a combined experimental and modeling study of microwave-activated dilute CH4/N2/H2 plasmas, as used for chemical vapor deposition (CVD) of diamond, under very similar conditions to previous studies of CH4/H2, CH4/H2/Ar, and N2/H2 gas mixtures. Using cavity ring-down spectroscopy, absolute column densities of CH(X, v = 0), CN(X, v = 0), and NH(X, v = 0) radicals in the hot plasma have been determined as functions of height, z, source gas mixing ratio, total gas pressure, p, and input power, P. Optical emission spectroscopy has been used to investigate, with respect to the same variables, the relative number densities of electronically excited species, namely, H atoms, CH, C2, CN, and NH radicals and triplet N2 molecules. The measurements have been reproduced and rationalized from first-principles by 2-D (r, z) coupled kinetic and transport modeling, and comparison between experiment and simulation has afforded a detailed understanding of C/N/H plasma-chemical reactivity and variations with process conditions and with location within the reactor. The experimentally validated simulations have been extended to much lower N2 input fractions and higher microwave powers than were probed experimentally, providing predictions for the gas-phase chemistry adjacent to the diamond surface and its variation across a wide range of conditions employed in practical diamond-growing CVD processes. The strongly bound N2 molecule is very resistant to dissociation at the input MW powers and pressures prevailing in typical diamond CVD reactors, but its chemical reactivity is boosted through energy pooling in its lowest-lying (metastable) triplet state and subsequent reactions with H atoms. For a CH4 input mole fraction of 4%, with N2 present at 1-6000 ppm, at pressure p = 150 Torr, and with applied microwave power P = 1.5 kW, the near-substrate gas-phase N atom concentration, [N]ns, scales linearly with the N2 input mole fraction and exceeds the concentrations [NH]ns, [NH2]ns, and [CN]ns of other reactive nitrogen-containing species by up to an order of magnitude. The ratio [N]ns/[CH3]ns scales proportionally with (but is 102-103 times smaller than) the ratio of the N2 to CH4 input mole fractions for the given values of p and P, but [N]ns/[CN]ns decreases (and thus the potential importance of CN in contributing to N-doped diamond growth increases) as p and P increase. Possible insights regarding the well-documented effects of trace N2 additions on the growth rates and morphologies of diamond films formed by CVD using MW-activated CH4/H2 gas mixtures are briefly considered.