Can Battle Master maneuvers also apply to special attacks?

Question

Battle Master maneuvers can give to-hit modifiers, attack advantages, damage bonuses and various effects to regular attacks.

My question is : can they do the same for Shoves (trips & pushes) and Grapples, which are classified as "special attacks" ?

Examples :

1. Applying a Precision Attack maneuver to a Shove-Trip roll;
2. Getting an advantage on a Grapple thanks to a Feinting Attack maneuver;
3. Using the Disarming Attack maneuver during a Shove-Push;
4. Adding the Menacing Attack maneuver effect to a Grapple;

etc.

Note 1 : although this question is related, it pertains to Pathfinder instead.

Note 2 : It is probably up to your DM whether a Shove can be made with a weapon, and although a Grapple must be made with a free hand, it is currently unconfirmed whether Battle Master maneuvers requiring a weapon can be applied to an unarmed attack.

Answer 1

No

Each of the maneuvers you have listed clearly state either

When you hit a creature with a [melee] weapon attack

or

When you make a weapon attack roll

Emphasis Mine.

Grapple, Shove, and Trip are all Athletics checks, not weapon attacks. Therefore, you are not making a weapon attack roll, or hitting with a weapon attack. You are performing an Athletics check to grapple, trip, or shove.

See the definitions of Grappling and Shoving a Creature on PHB 195, and Attack Rolls on PHB 194. A Grapple or Shove is a distinct type of attack from a Weapon Attack. The presence of 'weapon' in those maneuvers is there to indicate that the maneuvers only work when you make a Weapon Attack. Not when you make any attack.

This is the same rule that prevents things like grappling with Green Flame Blade, or Sneak Attacking with a Shove.