Yes the slip is a basic part of all the samba walks and results in the characteristic pelvic action.
This variant is (approximately) Stationary only because of the relative size of the forward step 1 compared with the slip. Each dance association has its own description but they are all very similar, the intention being that the dancers stays roughly on the spot.
For step 1 the IDTA says "close instep of LF to toe of RF".
The ISTD says "close LF to RF" but adds "may be repeated closing slightly forward on 1"