As noted above, Kepler’s Laws can be derived from Newton’s Laws. Planets in another stellar system would orbit in ellipses, and they would sweep out equal areas in equal times, because those are consequences of the gravitational force always pointing towards the central object and being inversely proportional to the square of the distance to the central object.
The Third Law holds too, with one caveat. The Third Law states that P[sup]2[/sup] = k a[sup]3[/sup], where a is the semi-major axis (see below) of the object, P is its period, and k is a constant that’s the same for all objects in a given stellar system. If you figure out what this constant is, it turns out to depend on the mass of the central object. So a different stellar system would have a different mass of its central object, and all the objects in that stellar system would obey P[sup]2[/sup] = k a[sup]3[/sup] with this new value of k.
And yeah, Kepler’s Third Law only depends on the semi-major axis, not the maximum distance. The semi-major axis of a comet’s orbit (or any other object’s orbit) is the average of its closest distance and its farthest distance. For a nearly circular orbit, this doesn’t make much of a difference. For Halley’s Comet, though, the semi-major axis is about the same as the semi-major axis of Uranus — and so they both go around the Sun in approximately 80 years.