No.
Let's work through this piece by piece. To start with, here are some basic definitions:
- An attack is a single to-hit roll and a single damage roll (PHB,
p. 194).
- On a character's turn, they can take one action, and (if they have abilities that permit it) a single bonus action (PHB, p. 189).
- One of the actions a character may take is the Attack
action, which allows them to make a single attack (as defined
above) with a melee or ranged weapon (PHB, p. 192).
Here's the general rule for fighting with two weapons (PHB, p. 195):
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.
Here's the Two-Weapon Fighting fighting style (PHB p. 91):
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.
Here's the ranger's Extra Attacks feature (PHB p. 91):
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
And here's the relevant parts of the hunter's mark spell (PHB, p. 251):
Casting Time: 1 bonus action
Duration: Concentration, up to 1 hour
You choose a creature you can see within range and mystically mark it as your quarry. Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack ... If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to mark a new creature.
So:
- The ranger can take the Attack action to make two attacks (one from taking an Attack action and one from Extra Attack). Each one (if it hits, and if the ranger used a dagger) will do 1d4 (dagger) + 5 (Dexterity) damage.
- If the ranger takes the Attack action, and they are wielding a dagger in their off-hand, they can use their bonus action to make one additional attack, also doing 1d4+5 damage. (The Two-Weapon fighting style allows them to add their Dexterity bonus to to damage).
- Hunter's mark takes a bonus action to cast or change targets. This means the ranger can't make a third (off-hand) attack on a turn when they cast it.
- Hunter's mark requires concentration to maintain, meaning the ranger needs to make a saving throw every time they take damage while concentrating on the spell (PHB, pp. 203-204).
- Hunter's mark affects one target. The ranger won't get any damage bonus against other targets.
So, to answer your specific questions:
Does having two daggers with Two-Weapon fighting allow attacking with both in a single action? No. The Attack action allows a single attack, regardless of how many weapons are being held. Two-Weapon Fighting only affects how much damage is done with the bonus action attack, not the number of attacks that can be made.
Corollary to the above, does Extra Attack allow another Attack action where he can attack with both daggers again? No. He can make two attacks with a dagger instead of one. Attacking with the second dagger requires using a bonus action.
Does he add the Dexterity modifier to the damage of every single hit? Yes. That's what the benefit of Two-Weapon Fighting is.
Does Hunter's Mark add 1d6 for every single hit? Yes, for every hit on the creature that was the target of hunter's mark after it was cast.
On turns after the the turn when the ranger has used a bonus action to cast hunter's mark, they can make three attacks (using their action and bonus action) against the targeted creature, and each of those attacks will do 1d4+5+1d6 damage.
