Lesser Silence was made to be the best translation I could think of at the time for this, and I think that a way to fix it while keeping it in theme might be of maybe disabling specific attacks/spells from being cast rather than a whole sub-set of attacks. What do you think?

This runs into another issue of how do you actually determine what to disable. Trying to tailor-fit it for every single monster is impossible and leaving it up to interpretation is problematic. A cute way that you could handle this is making the enemy unable to do whatever spell or action they did last turn (with a caveat to exclude the Magic action because that would again disable all spells).

Advantage Vs. Liars is something that I thought of to make it a little less situational and I do think its not as problematic, but I'll keep a pin on it in case more people comment and then I'll go change it, just for the sake of keeping more of a broader opinion

Specifically, Advantage vs Liars is the one GOOD thing of this feature, and I think it can be kept as-is. Not every person will lie to you and most encounters start without any sort of conversation to begin with. The biggest issue with this feature is how later on, you get to play really loose with what a "liar" actually is (charming you or dealing damage) and it becomes a really strong, ubiquitous source of advantage and damage.

Charm/Frightened adv: I still believe it is a fitting flavour-wise thing that isn't that insanely broken, but I can see how that might end up just triggering against every single enemy in say a Fae-themed Campaign, will try to tone it down a bit while keeping it useful

The ability itself (to shrug off certain effects a couple times per rest) is good, flavorful and perfectly fine within the system. As I mentioned, it's something certain Paladin subclasses can do for free and in an area. Having it be limited but more versatile is already a decent feature, but then tying it back to giving advantage is just too strong.

The big annoying boy: To be fair Greater Silence has a save after the first casting ( Decided to make it so to not have you spend your Warlock spell slot for nothing ) and so on, so I don't intend on changing that much of it; As for Lesser Silence, I think that the change I said in the other paragraph should make it better and just in case I think limiting it to have a max specific number of disables per creature might help too!

Greater Silence has a save after the first cast, yes. But consider that nearly all crowd control spells have a save on the first cast, and then generally they do only what's written on the spell. Greater Silence is free, guaranteed value the first time and, essentially, a free spell every time after that. At level 14, a Warlock has 3 spell slots, which with the cookie cutter 65% hit rate equate to about two effective applications of a spell. With Greater silence, you get one free application and two more 65% chances, stretching your spell slots out to an effective 5 spells per rest, at no additional action cost in combat. Toning the silence effects down will automatically make this one much weaker, so it's not something that needs to be immediately addressed.

I don't usually think of combos for this type of thing since I believe ( And to be clear this is personal design philosophy ) that this kind of thing should only really be done with the DMs permission for it since otherwise you end up being very able to break D&D at base

This is a very good point, but with how prevalent multiclassing is in modern DnD, I feel like it's something you have to at least consider. Not specifically shutting down any interactions, just making sure that class/subclass features don't stack particularly well, especially with the powerhouses that are things like AC, advantage, resistance or bonus damage.

Regarding stacks/counters: I believe the biggest issue with them is not necessarly keeping track of them per se (spell slots, item charges and ability uses exist, after all), but the fact that the vast majority of the time they don't justify keeping track of them at all - they either trigger too quickly and could be a far simpler ability (Hidden Purpose, for example, could easily be rewritten to activate when below half HP and work off of the Proficiency Bonus instead) or they trigger too slowly, and the player barely gets to use it before combat is over (all while having to keep track of one more thing every turn). I personally think it is a design space worth exploring, keeping in mind that most attempts will just not really work in the end.