When a loved one dies, is that the end of the relationship?

[Director Michael]

Is that connection between parents, grandparents, friends, all those we love, still intact after death?

It can be, depending on what happens to the departed soul. For most people in this world who have a loved one who passed on, even if that spiritual connection does remain more or less intact, it is not consciously felt or experienced.

(It needs to be mentioned that the passing of a soul into the spiritual realm, after the person dies, does involve a degree of separation from the physical realm which is required to be respected. In other words, necromancy and idolatrous rituals for calling up a departed soul are universally forbidden.)

Would they be 'with' us or 'aware' of certain events in our lives after their passing while we are left on earth?

They can be. Again, as above, it depends on what happens to the departed soul.

And after the resurrection in the World to Come, will we be reunited? Will we know each other?

For the souls of the righteous (which includes the sincerely repentant), who will be resurrected into the future World to Come, the answer is yes. As Rambam (Maimonides) informs us in "Laws of Kings" 8:11, "Any Gentile who accepts the Seven [Noahide] Commandments and is careful to observe them is of the 'pious of the nations of the world' and will have a portion in the World to Come."

Is this the same as being "gathered to our people"?

No. That refers to the soul of a person when he passes away. If the soul merits to then ascend to a spiritual reward in the Heavenly realm, it joins the souls of those of its previously deceased relatives who also merited to ascend to spiritual reward in the Heavenly realm.

In regard to this, the following "dvar Torah" was posted by netzach.org.uk:

"Finally, in 'Gevoros Hashem' the Maharal [of Prague] suggests as follows: We know that the good deeds of a son can give spiritual merit to his father. Even if the father is wicked, the good deeds of his son are still accounted in his favour. Such was the case, says the Maharal, with Avraham and Terah [his father] - Terah may have done little good during his lifetime, but he gained enormous merit through the actions of his son Avraham. So much so, that ultimately, the few good deeds Terah did possess, combined with the actions of his son, were enough to ultimately accept him as 'righteous'."
[I.e., after Terah died, his soul was accepted by the Heavenly Court as righteous enough to be permitted to ascend to the Heavenly realm. Then later, when the righteous Avraham died, his soul was "gathered to his people" - meaning, when Avraham died and his soul ascended to the Heavenly realm, the soul of his father Terah was there waiting for him.]

This "gathering up" of the meritorious souls after their physical death is a process which has been going on throughout the history of mankind. At the future time of the Resurrection, which is the beginning of the World to Come (the ultimate milestone of the future Messianic Era), the souls in the Heavenly realm which merit to be resurrected will return to re-created immortal physical bodies in the physical world, to forever experience an open revelation of  G-d.