Echo Knight multiclass damage calculations

I am currently working on a new character concept for an upcoming game and was unsure about what damages the Echo Knight’s echo would actually be able to do.

For this scenario, the build will be a Minotaur Zealot Barbarian 5 / Echo Knight Fighter 3 with the Great Weapon Fighting fighting style and Great Weapon Master feat.

Unleash Incarnation

You can heighten your echo’s fury. Whenever you take the Attack action, you can make one additional melee attack from the echo’s position.

Hammering Horns

Immediately after you hit a creature with a melee attack as part of the Attack action on your turn, you can use a bonus action to attempt to shove that target with your horns. The target must be no more than one size larger than you and within 5 feet of you. Unless it succeeds on a Strength saving throw against a DC equal to 8 + your proficiency bonus + your Strength modifier, you push it up to 10 feet away from you.

Great Weapon Master

You’ve learned to put the weight of a weapon to your advantage, letting its momentum empower your strikes. You gain the following benefits: On your turn, when you score a critical hit with a melee weapon or reduce a creature to 0 hit points with one, you can make one melee weapon attack as a bonus action. Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack’s damage.

Great Weapon Fighting

When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2. The weapon must have the two-handed or versatile property for you to gain this benefit.

So, there’s a few parts to this question

  1. If my character is currently raging when he manifests his echo would attacks made through the echo be able to apply rage and divine fury damage?
  2. When making the attack via the echo would the attack penalty and damage increase from Great Weapon Master be applicable?
  3. When rolling the damage for the attack would Great Weapon Fighting rerolls be applicable?
  4. Would the Minotaurs Hammering Horns ability to push the target?