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, you can use the tentacle attack and eldritch blast on the same turn

The feature - which is almost exactly the same as the Tentacle of the Deeps feature from the final Fathomless patron detailed in Tasha’s Cauldron of Everything - says:

As a bonus action, you create a 10-foot-long tentacle at a point you can see within 60 feet of you. [...] When you create the tentacle, you can make a melee spell attack against a creature within 10 feet of it.

And later:

As a bonus action on your turn, you can move the tentacle up to 30 feet and repeat the attack.

In both cases, making the attack is part of the same action that either creates or moves it. This is pretty explicit in the move. In the case of the initial creation, thanks to the principle that there aren’t any hidden rules in 5E, and the absence of any general rule that making an attack must always be an Action, the language “when you create the tentacle” indicates the attack is made as part of the same bonus action used to create it.

(Remember that the Attack Action is just one possible action, available to everyone, which allows a character to make an attack. An “attack” is the separate process of making an attack roll, comparing it to AC, and rolling damage on a hit. There are numerous other rules and features that allow attacks as bonus actions, e.g. the offhand attack made as part of the Two-Weapon Fighting rules.)

So in this instance, the attack is made as part of the same bonus action used to create or move the tentacle. As the feature doesn’t involve casting a spell, it doesn’t interfere with the user’s ability to cast other spells on their turn. So a character can, on the same turn, summon or move the tentacle and make an attack with it as their bonus action, and cast a spell with a casting time of 1 action, including eldritch blast.