We present 610 MHz and 2.1 GHz imaging of the massive SZE-selected z=0.870 cluster merger ACT-CL J0102-4915 (El Gordo), obtained with the GMRT and the ATCA, respectively. We detect two complexes of radio relics separated by 3.4 (1.6 Mpc) along the systems NW-to-SE collision axis that have high integrated polarizations (33%) and steep spectral indices, consistent with creation via Fermi acceleration by shocks in the ICM. From the spectral index of the relics, we compute a Mach number of 2.5^{+0.7}_{-0.3} and shock speed of 2500^{+400}_{-300} km/s. With our ATCA data, we compute the Faraday depth across the NW relic and find a mean value of 11 rad/m^2 and standard deviation of 6 rad/m^2. With the integrated line-of-sight gas density derived from new Chandra observations, our Faraday depth measurement implies B_parallel~0.01 mu G in the cluster outskirts. The extremely narrow shock widths in the relics (<23 kpc) prevent us from placing a meaningful constraint on |B| using cooling time arguments. In addition to the relics, we detect a large (1.1 Mpc radius), powerful (log L_1.4[W/Hz]= 25.66+-0.12) radio halo with a Bullet-like morphology. The spectral-index map of the halo shows the synchrotron spectrum is flattest near the relics, along the collision axis, and in regions of high T_gas, all locations associated with recent energy injection. The spatial and spectral correlation between the halo emission and cluster X-ray properties supports primary-electron processes like turbulent reacceleration as the halo production mechanism. The halos integrated 610 MHz to 2.1 GHz spectral index is 1.2+-0.1, consistent with the clusters high T_gas in view of previously established global scaling relations. El Gordo is the highest-redshift cluster known to host a radio halo and/or radio relics, and provides new constraints on the non-thermal physics in clusters at z>0.6. [abridged]
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