The "if you gain a 6th Luck point" thing is sensible for when the players are rolling, but it conflicts extremely hard with the DM awarding Luck points. You could easily be on 4 Luck and not have a chance to dump it - because you keep succeeding on rolls, and it makes zero sense to use unless you fail, or simply because you haven't made any rolls, then get awarded a couple of points for different things by the DM, and suddenly, through no fault of your own, you've lost all your Luck points.
The basic mechanic makes sense, but the problem is expanding it to being reward for "clever plans" or "daring achievements" or the like. You should only lose it if you'd gain it from a roll. Or there should be some other kind of point for "clever plans" and so on, that don't have a chance to back fire.
Very disappointed with the Fighter design. It's like, a very slightly better version of two WotC designs, but they were dumb designs. Manuevers should be a part of the Fighter chassis, and frankly, "magic dude" absolutely 100% should NOT be a base/common Fighter subclass, it's just an incredibly perverse approach. If you want to play a caster, play a caster.
And if you want there to be a magic-fighting hybrid, make a class for it, don't bloody ruin the Fighter chassis for it.