1) this question has no real answer as it depends on the reference frame being used. It is very unlikely that they will be stationary except in their own reference frame.
rephrased 1) In theory their paths can be calculated precisely if you know their speed and the positions and motions of all other bodies (also gas and dust clouds) that might influence their motion. Practically, you will not have that knowledge, as most non-stellar bodies that the rogue planet may encounter will be very dim and you will not be able to detect them. On the other hand space is for the most part empty, so you might reasonably expect their paths to be quite predictable (within a limited time frame). They'll probably be in orbit (either an elliptical, parabolic, or hyperbolic) around the centre of the milky way.
2) yes, they will probably have some angular momentum left from where they formed.
Space is very large so it is not very likely that one will appear in our solar system in our lifetime. And of course we do not know if none ever moved through the solar system.