It is 100% dependent on whether you think the Dueling Fighting Style applies to thrown weapons; a question already discussed elsewhere
If Dueling Fighting Style doesn't apply to thrown weapons then clearly these never stack as the Thrown Weapons Fighting Style requires a thrown weapon. Below I will show that if the Dueling Fighting Style does apply to thrown weapons then they do stack. Seeing as how the question about whether the Dueling Fighting Style applies to thrown weapons already exists, and answers argue both ways, there's no real reason to answer that question here.
The Dueling Fighting Style states:
When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon.
The only relevant thing this requires is that we attack with a melee weapon.
And the Thrown Weapon Fighting Style states:
You can draw a weapon that has the thrown property as part of the attack you make with the weapon.
In addition, when you hit with a ranged attack using a thrown weapon, you gain a +1 bonus to the damage roll.
This requires a weapon with the thrown property, and that we make a ranged attack using said weapon. The thrown property shows that a melee weapon, when thrown, is making a ranged attack:
If a weapon has the thrown property, you can throw the weapon to make a ranged attack [...]
All we need to do then is throw a melee weapon with the thrown property and we would benefit from both Fighting Styles.
Note that these do not add together when using a dart (or technically a net, but that has no damage roll anyhow) as they are ranged weapons with the thrown property, so Dueling can't apply.
I see no reason that the damage bonuses wouldn't stack, the only thing you cannot add twice to a roll (as far as I'm aware) is your proficiency bonus:
Your proficiency bonus can't be added to a single die roll or other number more than once.
A small note on wording:
The Thrown Weapon Fighting Style technically only requires a weapon with the thrown property if you're drawing it. The damage bonus applies to any ranged attack using a thrown weapon. This means that technically it applies to ranged improvised weapon attacks as well:
[...] An improvised thrown weapon has a normal range of 20 feet and a long range of 60 feet.
Note, however, that the Dueling Fighting Style would not apply because improvised weapons do not have the melee or ranged properties, they simply are weapons used to make melee or ranged attacks.
Yes.
You quoted the necessary text: "as if you were in the echo's space". It's not the echo making the attack, but you attacking as if you were in its space. As a further indication, spirit shroud has a range of self, so it would indeed benefit the opportunity attack you make as if you were in the echo's space.
For a contrasting effect, let's say you were within the aura created by the crusader's mantle spell cast by one of your allies and your echo is not. In this case, the opportunity attack made from the echo's space would not gain the benefits of this spell because you would not be within that aura since you are making it from the echo's space, even though "your real you" still is within it.
You can sort of see it as a quick and temporary teleportation effect.
Best Answer
Rules-as-written, looks like yes.
I'm not sure that it matters that the character is an Echo Knight; the same question would arise for any player with a two-handed ranged weapon and the Thrown Weapon fighting style.
Relevant rules excerpts and references:
Two-handed weapons: PHB, p147
Thrown Weapon Fighting: TCoE, p42
Other Activity on Your Turn: PHB, p190. Drawing or sheathing a weapon is explicitly mentioned as something you can do in addition to your action (which is relevant for putting the weapon away before attacking with the bow again).
Opportunity Attacks: PHB, p195:
It's not specified anywhere that you need to currently be wielding a melee weapon in order to make that attack, just that the attack itself is not ranged.
So, you don't need to hold a bow with two hands when not attacking with it (i.e. outside of your turn), you can draw a weapon with the thrown property as part of an attack whether you're throwing it or not, and you can sheathe the weapon again on your turn before attacking with a bow.