2 weapon fighting and a pact weapon et. al.

Assume a 1st level warlock.  The PC has Eldritch Blast and Pact Weapon invocation and light weapons

I assume I can have 2 light weapons to attack with and one is a Pact weapon so no issues with that.  One is during my attack action and one is during my bonus action.

I assume if my pact weapon is not light I can't use it for two weapon fighting.

Can I cast Eldritch Blast during my Magic action and swing a light weapon at a target (within 5 ft) in my bonus action?

What is the minimum range of Eldritch Blast? 

Can I correctly assume if I cast hex that Eldritch Blast fulfills the hex requirement "...damage to the target whenever you hit it with an attack roll. " 

Can I cast Hex in my bonus action then cast Eldritch Blast in my magic action? 

Is it a good idea though to do without taking the old hexblade subclass to wield one pact blade and one hexblade? 

I currently run a Paladin 1/Celestial Warlock X with the Pact Seeker (Infernal Pact) and wanted to work in Infernal Bulwark, so I went Fighter 1/Celestial Warlock instead for a slightly dexterous two-weapon fighting style. Is this a good idea?

www.dndbeyond.com/sheet-pdfs/Actionsparda_165040730.pdf

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Is it a good idea though to do without taking the old hexblade subclass to wield one pact blade and one hexblade? 

 

Honestly I would say no, just because I would hate having to keep track of two weapons that use different ability scores.

If you've got a level of Fighter, I'd be more inclined to take one higher-damage one-handed weapon as a Pact Weapon, put a shield on the other arm and take the Dueling fighting style.

 Unfortunately, Infernal Bulwark doesn’t work if you have a shield. Unfortunately, two-handed weapons aren’t really an option on a dexterous character. Is there a dexterity-based weapon lets you roll a D10 instead of a D8 if you hold it with two hands?

Quote from wagnarokkr >>

Quote from Actionsparda >>

Quote from wagnarokkr >>

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Is it a good idea though to do without taking the old hexblade subclass to wield one pact blade and one hexblade? 

 

Honestly I would say no, just because I would hate having to keep track of two weapons that use different ability scores.

If you've got a level of Fighter, I'd be more inclined to take one higher-damage one-handed weapon as a Pact Weapon, put a shield on the other arm and take the Dueling fighting style.

 Unfortunately, Infernal Bulwark doesn’t work if you have a shield. Unfortunately, two-handed weapons aren’t really an option on a dexterous character. Is there a dexterity-based weapon lets you roll a D10 instead of a D8 if you hold it with two hands?

Well, no, but you don't need Dexterity for a Pact Weapon; the attack and damage rolls use Charisma in that case.

 That’s true; dueling still requires you to be using only one attack, taking it from 1d8 + 7 to 1d10 + 5. Using dueling guarantees more damage too!

Thank you for your help!