[RPG] If I cast Hex on the familiar as a Pact of the Chain warlock, can I use the Relentless Hex eldritch invocation to teleport next to it

No.

Consider that:

Verbal (V)

...the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion.

If you can argue that this is ALL that is needed to cast a purely verbal spell, then anyone or anything with a mouth can cast it.

Let's get more basic: suppose you don't have spell slots left to cast Healing Word. Will speaking the words that produce "the particular combination of sounds, with specific pitch and resonance" set the magic in motion?

It all boils down to the power to cast it, and I'm afraid your familiar does not have it.

Let's look more closely, then, at:

Voice of the Chain Master

Prerequisite: Pact of the Chain feature

You can communicate telepathically with your familiar and perceive through your familiar’s senses as long as you are on the same plane of existence. Additionally, while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice, even if your familiar is normally incapable of speech.

There is nothing in there that ever mentioned -even vaguely- casting of any sort.

The argument of specific-beats-general here is also invalid because "specific" also denotes "explicit" and there is nothing here that explicitly and specifically grants you the power to cast verbal spells through the familiar. This case is more of a general-beats-vague.

Finally, the Find Familiar spell states the times when a familiar can (sort of) cast a spell:

Finally, when you Cast a Spell with a range of touch, your familiar can deliver the spell as if it had cast the spell.

Voice of the Chain Master lacks similar text that lets you cast verbal spells through it, so the feature can't let you do that.

What level find familiar is cast at depends on how the warlock casts it.

When she gains the Pact of the Chain class feature, the warlock learns find familiar. It doesn't count against her spells known, but nothing in the ability text prevents her from casting it with her spell slots. If she casts it with her spell slots, it works exactly like any other spell she knows how to cast. If she is 5th level when she casts it, she casts it as a third-level spell.

In addition, the warlock gains the ability to cast find familiar -- and only find familiar -- as a ritual. When a spell is cast as a ritual, it always uses the normal spell level of a spell. When the warlock casts find familiar as a ritual, she casts it as a first-level spell no matter what her warlock level may be.