**Q1:** The status of Post's 3-tag system as of 2011 was reviewed by Liesbeth de Mol in <A HREF="https://hal.univ-lille3.fr/hal-01396517/document">On the complex behavior of simple tag systems. An experimental approach.</A> *"It is still not known whether this particular example has a decidable reachability problem."* <A HREF="https://scholar.google.com/scholar?client=safari&rls=en&oe=UTF-8&um=1&ie=UTF-8&lr&cites=6491146449059987717">Citations</A> to this work through 2017 indicate that the situation has not changed since 2011.

**Q2:** Concerning cycle structures, De Mol found additional cycles:

> Let $a = 00$, $b = 1101$. Watanabe deduced wrongly that there are only four kinds of periodic
> words in Post’s tag system, i.e., $a^2b^3(a^3b^3)^n$ with period 6, $ba$ with
> period 2, $b^2a^2$ with period 4, or any concatenation of the last two. In
> some preliminary runs on Post’s tag system we found three other kinds
> of periodic words, a period 10, 40 and 66. The period 10 $(b^2a^3b^3a^2)$ is
> similar to the periodic words found by Watanabe, the period 40 and 66
> are very different from these periodic words.