If you choose to use 2 martial weapons instead of 1 and a shield are you able to role for a hit with each weapon? 

Here is the relevant information on Two Weapon fighting, this is without any Feats which can make this play style more effective.

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. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.

thank you very much

When you get extra attack at level 5, you can attack with both weapons during the normal attack and apply modifier to damage with both (they also don't need to be light).

The bonus action attack doesn't change from this though. You can get 2 weapon fighting style at level 2 to add modifier to bonus action attack. The dual wielder feat is needed to be able to use non-light weapons and make bonus action attack.

It may be an ethical question as well. Would a Paladin choose to fight with two weapons. A matter of honor.

Back in the day we were more concerned with ethics for paladins and I'm sure we would have allowed it back then.  The key back in those days was the paladin had to salute his opponent before he could assume his stance and begin combat.  Nobody bothers with that sort of thing anymore.

A paladin (back in the day) was about chivalry and would’ve wanted to proudly show his crest on his shield.  Two weapon fighting was dishonorable 

I thought about the honor aspect of it, but we are starting a new campaign and I wanted to try a Paladin and take the oath of vengeance. I thought maybe honor wouldn't have as much to do with that.

Knights (Paladins) typically fought in and against heavy armor. Two light swords wasn't doing much for you.

You can spin your Paladin as more of a samurai style. Many Asian martial arts used two-weapon fighting.

I have a MC vengeance pally / swashbuckler that is a lot of fun.

I don't think there's any real ethical concerns here unless there's something very specific to your paladin's order, if they're even part of an order. 

I think using a two handed weapon tends to out damage dual wielding to my understanding, but so long as your build isn't reliant on using bonus actions for other things frequently, two weapon fighting should be good enough. 

I just wanted to see this thread and point out - many paladins have two hands.

Bad joke... moving on. :D