A: There are several different ways this can be handled: one situation is that you have a base tax year and as tenant are responsible for any and all amounts over that base amount. Another scenario that the Tenant is liable for all of the taxes and associated costs. Finally, and unlikely, the tenant could have zero exposure for taxes, but that’s rare. To sum it up it is whatever you negotiate with the Landlord prior to signing any lease.
A: I would want to double-check your lease. Often times there is a no-pet provision under the rules section. Further, unless you are planning a legitimate registered service animal, I would get written permission for your future protection.
A: In short, you would “step I to the shoes” of the prior owner. That said, you must be careful with your due diligence to make sure what your stepping into works for you.