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.

No.

Or, more specifically, yes, as long as you didn't get those features via multiclassing, which is never.

The multiclassing rules state:

Extra Attack
If you gain the Extra Attack class feature from more than one class, the features don't add together. You can't make more than two attacks with this feature unless it says you do (as the fighter's version of Extra Attack does). Similarly, the warlock's eldritch invocation Thirsting Blade doesn't give you additional attacks if you also have Extra Attack.

Since you only get Extra Attack as a Warlock if you multiclass and you only get Thirsting Blade as a non-Warlock if you multiclass, this rule always applies and you can never use them together.

Furthermore, even if you did find a way to get them both from a single class, you couldn't use them with two-weapon-fighting like that because the bonus action attack from two-weapon fighting isn't an Attack action. You could, however, use them together in that case despite the 'twice' language to get three attacks out of a single attack action without issue: just make your first attack with something other than your pact weapon and then use your pact weapon via Extra Attack and then use it again via Thirsting Blade. Again, though, you can't actually do this because no class has both class features and they don't stack when you multiclass.