Should be this one. SC cable
this show pictures with different connector types to choose from
Hey there. I install fiber for att and you want a sc connector fiber jumper. This one off Amazon should work fine. PacSatSales - Fiber Optic Patch Cable - Single Mode - SIMPLEX - OS1-9/125um (10M, SC/APC to SC/APC) https://www.amazon.com/dp/B01GIWE88S/ref=cm_sw_r_cp_api_i_.kK6EbY858MEZ
Amazon has what looks like replacement Fiber cables if you want to try to replace it yourself.
this is an ideal install.
the extra fiber in the box is a service loop and is best practice.
if you wanted to move the gateway, i would leave the PON adapter where it is, and relocate the gateway with a new patch cord ran to where you want it. https://smile.amazon.com/PacSatSales-Single-SIMPLEX-Fiber-Optic/dp/B01GIWE88S
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personally, i would just turn off the wifi, and bridge the gateway if possible and use my own equipment, that metal box isn't helping your wifi...
32ft cable:
Cool, looks like it's an SC/APC connector, you'd need something like this https://www.amazon.com/APC-Fiber-Optic-Patch-Cable/dp/B01GIWE88S/ref=sr_1_3?keywords=sc%2Fapc+10m&qid=1555382487&s=gateway&sr=8-3