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Nearby, low-metallicity dwarf starburst galaxies hosting active galactic nuclei (AGNs) offer the best local analogs to study the early evolution of galaxies and their supermassive black holes (BHs). Here we present a detailed multi-wavelength investigation of star formation and BH activity in the low-metallicity dwarf-dwarf galaxy merger Mrk 709. Using Hubble Space Telescope H$\alpha$ and continuum imaging combined with Keck spectroscopy, we determine that the two dwarf galaxies are likely in the early stages of a merger (i.e., their first pass) and discover a spectacular $\sim 10$ kpc-long string of young massive star clusters ($t \lesssim 10$ Myr; $M_\star \gtrsim 10^5~M_\odot$) between the galaxies triggered by the interaction. We find that the southern galaxy, Mrk 709 S, is undergoing a clumpy mode of star formation resembling that seen in high-redshift galaxies, with multiple young clusters/clumps having stellar masses between $10^7$ and $10^8~M_\odot$. Furthermore, we present additional evidence for a low-luminosity AGN in Mrk 709 S (first identified by Reines et al. 2014 (arXiv:1405.0278) using radio and X-ray observations), including the detection of the coronal [Fe X] optical emission line. The work presented here provides a unique glimpse into processes key to hierarchical galaxy formation and BH growth in the early Universe., Comment: Accepted for publication in The Astrophysical Journal March 5, 2021. 14 pages, 7 figures