Electron-paramagnetic-resonance studies of the dilute two-dimensional antiferromagnet ${\mathrm{Rb}}_{2}{\mathrm{Mn}}_{c}{\mathrm{Mg}}_{1\ensuremath{-}c}{\mathrm{F}}_{4}$ are reported versus both concentration and temperature. Particular attention has been paid to the temperature-dependent resonance linewidth near the percolation threshold, $c\ensuremath{\simeq}{c}_{p}=0.59$, where a variety of interesting effects are observed: At high temperatures the linewidth is dominated by the long-time, $q\ensuremath{\rightarrow}0$ diffusive part of the dipolar interaction having ${(3{cos}^{2}\ensuremath{\theta}\ensuremath{-}1)}^{2}$ anisotropy characteristic of two-dimensional systems. This contribution increases rapidly below the percolation concentration due to slowing of spin diffusion as the spin network breaks up into finite clusters. For $Tl30$ K and $c\ensuremath{\sim}{c}_{p}$ the linewidth is dominated by antiferromagnetic correlation effects leading to rapid line broadening as $T$ decreases and a change of anisotropy. Both effects are only crudely described by the RPA theory. For $cl{c}_{p}$ most of the resonance intensity remains centered at $g=2$ down to the lowest temperatures reflecting the absence of long-range order. Near and above ${c}_{p}$ and for $Tl4.2$ K some intensity is shifted to lower fields, however, as the percolation cluster orders. Most remarkable is the appearance of a nine-line superstructure on the $g=2$ resonance at 1.6 K in samples near the percolation concentration. This illustrates the critical slowing of spin dynamics on a time scale of ${10}^{\ensuremath{-}9}$ sec and is believed to be the resonance of spins surrounded by nonmagnetic nearest neighbors but coupled to next-nearest-neighbor spins, most of which are locked to clusters. Evidence of anisotropic spin fluctuations and the possibility of reduced next-nearest-neighbor exchange or very large zero-point spin deviation is found in this regime.