**Q1:** The state of the art as reported in 2014, see <A HREF="https://arxiv.org/abs/1406.2097">arXiv:1406.2097</A>, is that the only numbers which are known to be Tarski numbers of some groups are 4,5,6. Tarski numbers $<4$ are forbidden, which suggests that 7 is the answer to the question *"What is the smallest non negative integer that we do not know yet is the Tarski number of a group?"*.

**Q2:** Recent progress, in addition to the references by Manuel Norman: In <A HREF="https://arXiv:1603.04212">arXiv:1603.04212</A> it is shown that the Tarski number of Burnside groups is in the range $[6,14]$.