No, You cannot combine attacks with booming blade.
Both Booming Blade and Green Flame Blade say the following:
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range
This means that these cantrips do not require you to take the Attack action, they require you to take the Cast a Spell action.
If we look at extra attack, it is defined as:
Beginning at 5th level, you can Attack twice, instead of once, whenever you take the Attack action on Your Turn.
No Attack action is taken, so no extra attacks can be used. Additionally, two weapon fighting states:
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.
Again, no attack action is taken, so you cant use a bonus action to make an off hand attack.
In your scenario, you can cast hunter's mark or hex, and then the hit from the booming blade will trigger those effects, as well as sneak attack (if the conditions are met), but you will be unable to make more attacks after that.
Action surge gives you another whole action, which you can use to cast a spell, like Booming Blade which will give you one more attack, or if you just use a regular attack action, extra attack and two weapon fighting could apply.
If you are hidden from the target at the time of casting then you get advantage:
Unseen Attackers and Targets (PHB p.194)
When a creature can’t see you, you have advantage on attack rolls against it.
The green flame blade spell, as an example, has this in the description:
Green-Flame Blade (Sword Coast Adventurer's Guide p.143)
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails. On a hit, the target suffers the attack's normal effects.
The action taken to cast the spell is also the action that "contains" the attack. If the target is unaware of the caster at the time of casting they are equally unaware of the caster at the time the attack is made.
Therefore the attacker has advantage on the attack roll and may use sneak attack.
Best Answer
No, because Cast a Spell and Attack are different actions.
Green-flame blade says,
When you cast this spell, you are taking the "Cast a Spell" action. As part of that action, you make a melee attack.
On the other hand, you must take the "Attack" action in order to use your extra attacks: (the Monk, PHB 79)
Because casting Green-Flame Blade is not the Attack action, you don't get to access your multiple attacks.
As a comparison, grappling explicitly states that you can grapple as one of your multiattack attacks (PHB 195):
If Green-Flame Blade worked this way, it would say so as well.