Where it states that the Buyer pays for all "transfer taxes", this is referring to the tax that is charged when the ownership of a property is transferred from the previous owner to you, the buyer. In typical sales, payment of the transfer tax is divided equally between the seller and the new buyer, but with foreclosed homes like this one, sometimes the buyer will need to pay the whole transfer tax and not just half; hence, the remark you see here. It does not mean that you will need to pay back taxes.
The answers to your questions are going to depend on the regulations of the area in which the property is located. The amount of the transfer tax, as well as the area's zoning requirements that would dictate which types of tests and permits are necessary, vary by location. FYI, there may also be additional fees you need to pay that are not mentioned here, depending on how you purchase the home (i.e., cash or mortgage, etc.). You would do best to contact an agent to represent you (I recommend an Accredited Buyer Representative). That agent will show you a complete lists of all the costs you would incur in the purchase of this home, before you sign a contract to purchase it. The agent will also be able to tell you what the area requirements for permits and tests are as well. Please feel free to contact me for help with the specifics, and good luck!