2) No, in fact when the number of crossings reaches infinity, the probability that there is a projection for some notation, tends to 0. We shall leave this discussion for later. Now we shall only mention that if a notation is drawable, and if the corresponding knot shadow is a connected sum of k prime shadows, there are (at most) 2^k possible projections. For more on this subject, click here.
3) It depends on the kind of the Reidemeister move.
4) It is possible to apply color tests and to obtain the Alexander polynomials from this notation; in order to obtain the more recently invented knot characteristics one would first have to obtain the braid whose closure is the denoted knot projection.
Charilaos Aneziris, email@example.com
Educational institutions are encouraged to reproduce and distribute these materials for educational use free of charge as long as credit and notification are provided. For any other purpose except educational, such as commercial etc, use of these materials is prohibited without prior written permission.