2. His eldritch blast is not a blast. Instead, it goes through his blade. Meaning he can't do ranged attacks, but his melee damage is weapon + eldritch + hex + Cha (if he takes the appropriate options).
Never heard about this ...
As far as i know, Pact of Blade Warlocks are not using Eldrich Blast regulary, its only their option in case they need to switch to ranged attack ...
They also dont use Eldrich invocations for it, but have their own ...
First worth noticing will be Thirsting Blade (lvl 5) ... allowing them to attack twice, instead of once with meele attack.
And second is Lifedrinker (lvl 12) ... allowing them to use deal another Necrotic damage equal to their Charisma modifier (min 1)
So final Calculation for damage is: Weapon Damage + Str/Dex Mod + Cha Mod + Hex ...
Meaning: (1d8 for Rapier ... Not sure how this works with +1 Rapier, but presuming it gives +1) + (+2 if he would have at least 14 Dex, wich also incerase his AC) + (up to 5, since you want your Charisma as big as possible on any Warlock) + (1d4 for every hit you land ...)
//Edit:
Not bad if you ask me ...
But i would still preffer safety of ranged attack combined with fact that on level 11 your Eldrich Blast allready have 3 beams (that can be used on same targets and every single one of them is triggering Hex) ...
and your Pact of the Blade still have single attack only (until next level, when you have to pick Lifedrinker to only get second strike).
//Edit:
My misstake i switched those Eldrich invocations in my mind and thought you get second attack at level 11, while you get it on level 5.
Anyway you dont get third meele attack ever (as far as i know at least) so rest of my point still stands.
