[RPG] Does the Ranger’s Favoured Foe Ability from Tasha’s work with Cantrips

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.

Yes, They stack.

5th edition has a lot fewer additive bonuses than some previous editions, and therefore does not need to prohibit the few circumstances where you get multiple bonuses. The biggest "gotcha" is making sure that you aren't getting the same bonus from two sources (you can't have two castings of Bless active on you, for example).

It is also worth noting that 5e does not have typed bonuses the same way that some other editions did (circumstance, skill, enhancement, etc.). Bonuses are just bonuses. Add 'em up.