This is my Nero600 which is the only fig that I haven't killed. My other trees all died when I placed them outside too early and the PNW decided to throw one last frost at us. That kinda bummed me out.  

Now that I'm done with the military I can focus on school and getting a house with my own backyard. The landlord don't like when I put the tree on his grass to get full sun. That way I can give my tree(s) better care. 

I have been giving the tree some all purpose plant food, worm casting juice, and fish poop from my aquarium hoping to supply it with the 17 nutrients it needed. I also tried other fertilizers here and there that had more P and K since everything else seemed to be high in N. She started to put out fruit a few months ago which didn't happen the year before so I was happy. However all the figs are bursting at the walls, deformed and leaking. I thought it was birds or bugs, but I haven't seen any at all. 

So I'm guessing I'm lacking a nutrient for proper fruit production causing the weak skin. Would it be better to pinch them off and let the tree focus on growth before winter? I'm not against that ideal since the fruits look too damaged anyways.  

Looks like all that new growth at bottom is new growth from this season. My experience has been that new growth from soil level does not produce much fruit if any as the plant puts all its energy into growth rather than fruit production. What you might need to do is to prevent your tree from freezing before anything else.
Storing it properly in winter would help and fertilize most importantly early in spring. Over fertilizing does not produce more fruit and might damage the tree.
Based on my two year old tree, this year this variety produces fruit near the top of branch in clusters, and you need to make it branch without pinching the top during the growing season, in order to see fruit. So if you wish to manage form, prune it during dormancy rather than pinch this one.
Someone else might have more experience as to how to grow this variety in a cold zone. In TX and unprotected in pot, this tree does not freeze and produced some nice figs just after two seasons. Thank You for your service.