In the first part of this research we extensively investigated and carefully determined osculating, original (when entering Solar system) and future (when leaving it), orbits of 22 near-parabolic comets with small perihelion distance (q(osc) < 3.1 au), discovered in years 2006-2010. Here, we continue this research with a detailed study of their past and future motion during previous and next orbital periods under the perturbing action of our Galactic environment. At all stages of our dynamical study, we precisely propagate in time the observational uncertainties of cometary orbits. For the first time in our calculations, we fully take into account individual perturbations from all known stars or stellar systems that closely (less than 3.5 pc) approach the Sun during the cometary motion in the investigated time interval of several million years. This is done by means of a direct numerical integration of the N-body system comprising of a comet, the Sun and 90 potential stellar perturbers. We show a full review of various examples of individual stellar action on cometary motion. We conclude that perturbations from all known stars or stellar systems do not change the overall picture of the past orbit evolution of long-period comets. Their future motion might be seriously perturbed during the predicted close approach of Gliese 710 star but we do not observe significant energy changes. The importance of stellar perturbations is tested on the whole sample of 108 comets investigated by us so far and our previous results, obtained with only Galactic perturbations included, are fully confirmed. We present how our results can be used to discriminate between dynamically new and old near-parabolic comets and discuss the relevance of the so-called Jupiter-Saturn barrier phenomenon. Finally, we show how the Oort spike in the 1/a-distribution of near-parabolic comets is built from both dynamically new and old comets. We also point out that C/2007 W1 seems to be the first serious candidate for interstellar provenance.
