My DM says I need a skill or feat to use my pact weapon and conjure weapon at the same time. Is this true? Because I want to dual wield warlock hexweapon but warlocks don't have anything that grants bonus actions?
Edit: This is different from other dual wielding because my weapon changes to a CHA modifier. Also the post linked still gives me two answers that arent specific to Hexblade class.
Every single character in the game can use two weapon fighting by meeting two conditions:
When you take the Attack action and attack with a light melee weapon that you're holding on one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. (PHB, 195)
weilding two light weapons
not using another bonus action on their turn
There are no other barriers to entry. It is possible your DM is thinking of previous editions of D&D or Pathfinder where this was the case, but in 5e it is not.
Warlocks do get bonus actions under the same conditions as everybody else:
You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. ([PHB][4])
Since you are using the Two-Weapon Fighting feature of the game, as long as you meet the conditions therein (having two light weapons), you are able to take a bonus action.
You do only get one bonus action per turn no matter what, so you cannot attack with both weapons if you've already used that on your turn. But otherwise, Yes you can easily use a bonus action to attack with the weapon you touch and the pact weapon you conjure.
The only thing the feat would do for you would be to allow you to use two weapon fighting with non-light weapons (and a couple of other good benefits).
tl;dr as long as you are wielding two light weapons you can use the two weapon fighting feature with no feat needed
"This is different from other dual wielding because my weapon changes to a CHA modifier."
This is not true. Using Two-Weapon Fighting (not dual wielding) has nothing to do with what modifier you use. The only thing it entails is having two light weapons and using a bonus action to attack with the other one as a bonus action.
Reading through this Twitter discussion might also help.
All characters can effectively dual wield and fight with two weapons so long as both of the weapons being held have the light property. The Player's Handbook describes how this works on page 195.
Two-Weapon Fighting
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. (PHB, 195)
There is no need for any feat, skill, or class feature to do so. This is a base action that all characters can use.
I assume your DM is referring to the feat Dual Wielder. This only is necessary if you are attempting to dual wield and attack with a non-light property weapon. For example, if you wished to dual wield two longswords, you would need to have the Dual Wielder feat.
As for if your DM is correct, well, that depends on what weapons you are attempting to dual wield. If you are attempting to dual wield and attack with two light weapons, he is wrong and you may do so with no feats or skills. If you are attempting to dual wield and one of your weapons does not have the light property, he is correct and you must acquire the Dual Wielder feat first.
All characters get bonus actions. There is no rule in the official books that states warlocks do not get bonus actions. This is described on page 189 of the Player's Handbook.
Bonus Actions
Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. ... You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. (PHB, 189)
Emphasis mine.
Since the Two-Weapon Fighting feature states that "you can use a bonus action", you get a bonus action. Your class does not matter.
If your DM continues to insist that Warlocks do not get bonus actions, ask them to explain how you use the Hexblade ability Hexblade's Curse, which requires you to use a bonus action.
In regards to your edited addition:
Dual wielding is the same for you as everyone else. It does not change what modifiers you use. If you have the ability to use Charisma as your attack stat with melee weapons, you can continue to do so while dual wielding.
