Okay, so looking at manoeuvres. I'll only comment on any if I have something to say. If I would just say "it's fine" without any clarifying remarks, I won't write anything at all.

First, a general remark on saving throws: having defined a generic saving throw DC to use, you really should just stick with it. Anything where the saving throw replaces your proficiency bonus with the manoeuvre die will be a little too good early on, and far behind the DC curve at high levels.


Sand Throw: I would consider allowing this to either require only an attack roll or a saving throw, but not both.

Weapon Throw: It's clear from context that this attack isn't treating the weapon as an improvised weapon, but it might be for the best, all the same, to explicitly specify that (a) you are proficient with the attack roll, and (b) you roll the weapon's normal damage die on a hit.

Repositioning Attack: This is fine, although the wording is a bit clunky. Maybe try:
When attacking a creature within 5 feet of you, you can expend one maneuver die to make a repositioning attack. On a hit, add the maneuver die to the attack's damage, and you and the target switch places.
Flying Kick: This is giving you a bunch of extra movement, potentially. I'm a bit concerned that someone who has, say, grabbed a level of rogue for expertise in Acrobatics could get some serious mileage out of this. I would consider capping the additional movement at 10 or 15 feet. After all, in theory, you could use this multiple times in a round (twice if you're a monk).

Somersault: Okay, this is almost identical to flying kick in terms of its effect; the movement is just happening after the attack instead of before. It's also not particularly useful for monks, who have Step of the Wind, while anyone who doesn't have tavern brawler isn't likely to find this ability useful.

Straight Kick: You should be able to boot anything smaller than you, so I would change the effect such that it affects any creature no more than one size larger than you. You might even want to be able to kick things that are two or more sizes smaller than you even further away.

Pin Down: This is burning your bonus action, but it's also restraining the target, so should be fine.

Rend Armor: I wouldn't let this work on natural armour. If nothing else, you can't use mending on it. Also, armour doesn't give an AC bonus in the style of 3.5, so the wording needs some work. Finally, surely non-magical repairs can also work? Maybe try:
[...] If the enemy is wearing manufactured armor, reduce its Armor Class by 1, to a minimum of 10 + its Dexterity modifier until a creature spends 1d6 hours repairing the armour or casts mending on it.
Pierce: Wording quibble: "move action" isn't a thing. I'd consider having the effect trigger anytime an affected target moves more than 5 feet on its turn. Also, the damage needs a damage type.

Pushing Attack: It's a bit tedious having duplicate abilities - this is very similar to Straight Kick, except this is strictly worse because Straight Kick just works on a hit while this also gives the target a Strength saving throw. I'd consider renaming Straight Kick to be more generic and allowing you to use it with any melee attack.

Tide of Steel: Easily the strongest ability on account of the AoE knockback. As it is, you already have two such abilities that affect a single target. Maybe this could do something else?

Cleaving Attack: Not a fan of "one-fifth" division. It really doesn't jive with the 5e design aesthetic. I'd just deal damage equal to the manoeuvre die.

Ricochet: Fiddly and annoying. I would just ignore some amount of cover.

Snipe: I would consider having the target make a saving throw as part of the attack, no matter what you target:
- head: on a failed save, target is stunned until end of its next turn
- body: not sure for this one, but maybe on a failed save, you roll one additional weapon damage die
- legs/wings: since the effect has no strict endpoint (either it makes the save or receives magical healing or the effect continues), this is fine
- arms/other limbs: the current effect is okay, but meh - I'd go with disadvantage on attack rolls and ability checks using the affected limb, and the affected limb can't be used to provide somatic components for a spell

Trip Attack: Couldn't you batter an opponent prone with your maul as well? Why restrict heavy weapons from working?