The Repelling Blast Invocation applies to each hit
Since we know you can select the target of each separate Eldritch Blast ray separately , even to the extent that other Repelling Blasts could actually push the same creature out of range of the remaining subsequent beams, we must rule that Eldritch Blast (no matter what Invocation is attached to it) is a single spell that hits in sequence, not simultaneously as per Magic Missile.
This is further expanded upon when we look at Hex, which triggers each time an attack hits the Hex'd target.
So the only conclusion the sound logic and readings of these rules can give us is that Eldritch Blast, Scorching Ray, and similar spells that require multiple attack rolls to hit their target(s) are NOT simultaneous and always hit independently of each other, in succession, unless otherwise noted in the spell's description.
As you pointed out, the prerequisite for Repelling Blast is:
"...When you hit a creature with eldritch blast..."
Eldritch Blast requires you to determine if you hit or miss each target or targets for each beam (not once per spell), thus letting us know if the requirements 'when you hit' or met or not. Repelling Blast, and any other feature, trait, spell, or spell-like ability that activates when hit or attacked by something would trigger for each Eldritch Blast beam.
So yes, at 5th level with 2 beams you could push a single goblin up to 20ft away, or push 2 different goblins up to 10ft away from you in a straight line. You do not need a separate ruling for hitting the same creature with multiple beams, because your ruling is already included in the spells text.
Yes
Using the 5E rule of specific over general, Green Lord's Gift does not call out specific ways of regaining hit points. The general case is "any". It doesn't hurt that Green Lord's Gift uses the word "any", either.
Green Lord's Gift was published as Gift of the Ever-Living Ones in Xanathar's Guide to Everything, p. 57. The prerequisites have changed, but the effect is the same:
Prerequisite: Pact of the Chain feature
Whenever you regain hit points while your familiar is within 100 feet of you, treat any dice rolled to determine the hit points you regain as having rolled their maximum value for you.
Best Answer
No, you do not need to know fireball - the language of "you can cast" enables you to cast it through this feature regardless of whether or not you know the spell. This invocation uses the same language as the ones that allow you to cast spells the warlock usually cannot learn, such as Dreadful Word or Ascendant Step.
To supplement this answer, note that it specifically has a spell known prerequisite of only eldritch blast, not eldritch blast and fireball. It would likely state the latter if it required that you knew fireball in order to make use of it.