Property taxes in NJ are due on the 1st day of the 2nd month of the quarter. Taxes are due 2/1, 5/1, 8/1, 11/1. When you pay taxes on 11/1 they are for October, November and December

You are bound by the terms of your original lease when it comes to notice. In my opinion the "code violation" doesn't play a role at all.

In my experience it really depends on how much commercial space there is. Meaning what percentage of the building is commercial. Typically lenders do not want to see more than 10% of the building being commercial. Talk with a mortgage broker(yes broker) rather than directly with a bank. Banks can only offer very limited product while a mortgage broker can shop the loan around to several different lenders. There are lenders out there that will lend in buildings with a higher concentration of commercial without raising the percentage of your down payment or raising your rate.

No, I am not a mortgage broker.

Good luck

It's not that easy(maybe not even possible) to challenge this. You need to read the PILOT agreement. In my opinion, you are not able to petition for a reduction.