Mechanically, it can't

Similar to the argument here, the Mage Hand has no stat block, it has no AC, no HP, so it doesn't make much sense to consider it attackable. Thinking in game terms, it's neither a creature nor an object, which are the usual targets for spells or attacks.

As a comparison, check Bigby's Hand:

The hand is an object that has AC 20 and hit points equal to your hit point maximum. If it drops to 0 hp, the spell ends. It has a Strength of 26 (+8) and a Dexterity of 10 (+0). The hand doesn't fill its space.

So, if the "thing" created by a spell is supposed to be targetable, something on these lines should be written.

As the DM would have to "make up" an AC and HP for it, as well as the consequences for its HP reaching zero, it's clearly intended that it can't be a target, since Spells only do what they say. Further indication of it is that the conditions when the spell ends are clearly defined:

The hand lasts for the duration or until you dismiss it as an action. The hand vanishes if it is ever more than 30 feet away from you or if you cast this spell again.

Meaning that reaching 0 HP shouldn't mean it would vanish (as the only written conditions for vanishing are these).

It... might?

Now, rethinking my answer, there is one thing: the lack of AC and HP doesn't mean something can't be "targeted". A creature could decide to "attack" the air, or the water in a river or the ground, with no effects whatsover. The same could be ruled to the Mage Hand - creatures could try to target it and attack it, it just would be the same as attacking nothing.

Now, would they? In most situations, I wouldn't rule that my creatures decide to attack the hand, since wasting their actions for nothing would make the cantrip stronger than it should be.

So, even though it is technically possible that the creatures choose to attack it, usually they shouldn't, mainly from metagaming/balance perspective.

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.