Not sure if this has been asked bfore (Or if i am asking the right way) 

Have i worked this out right or am i over looking something , please advice :) 

A Fighter level 5 / Ranger level 3 - Gloom Stalker useing a great weapon dureing Dread Ambusher.

1st Action Attack = 1st normal attack/ that then triggers another attack from Dread Ambusher / 2nd normal attack 

Use Surge to gain another action still on the 1st turn.

2nd Action Attack = 1st normal attack/ that then triggers another attack from Dread Ambusher / 2nd normal attack 

As the 2nd action is still in the 1st turn of combat dose it also get the additional weapon attack as part of that action, as i do not see any limit to +action/attack.

As the additional attack is not useing your Bonues action you still have that open for later. meaning (if you had the Great weapon master Feat, witch grants you another attack useing your bonues action) this Fighter could have 7 great weapon attacks on the 1st turn of combat.
Then from turn 2 onwards it would get only 2 attacks per turn, 3 if he crits or take someone down to 0 HP due to Feat.

Dread Ambusher
At the start of your first turn of each combat, your walking speed increases by 10 feet,
which lasts until the end of that turn. If you take the Attack action on that turn,
you can make one additional weapon attack as part of that action. If that attack hits, the target takes an extra 1d8 damage of the weapon’s damage type.


Sorry for any spelling mistakes.
Not sure if i am missing somthing but any advice on this question will help alot thank you. :) 

This would be correct as nothing in the feature limits it to once per turn.

For every attack action you take you get the extra attack.

Since you are using the attack action twice then you get the ambusher attack twice.