I'd kinda prefer Bug stick with the multi-strike effect, but change it to 2 hits that are both half-strength -so they get the Sub-breaking, Sash-bypassing, extra secondary effects stuff, but not to an extreme degree and with no firepower increase. Interesting, but not broken. Also, it provides only minimal improvement to Mega Heracross, vs the current version letting it get tougher and heal up at no movepool cost...
Anyway, as far as the current set of effects...
Team Player: Seems gimmicky.
Necromancer: Seems even more gimmicky.
Reckless Abandon: Basically Fighting types are really really good at wallbreaking but not so good at the sweep -50% recoil is huge, and means most Fighting types will KO themselves in short order, possibly even if they're running Drain Punch. Also, if they run into a wall they can't shove aside, they'll kill themselves in short order. Life Orb and Guts abusers in particular melt like butter.
Flying Blows: Still a weird effect. The obvious thing to do is to run Return/Frustration -not only because they're strong but because Normal and Flying overlap pretty heavily in offensive parameters. Being double-resisted by Rock and Steel is annoying, but usually you'll just switch to a coverage move anyway. (Landorus-Therian will just smack Aggron with Earthquake and be done with it)
Hazardous Waste: Screw Toxic, Imma Poison Jab you and it's Toxic, and it works 100% of the time, and screw your Magic Bounce. In fact, screw it completely, it's gone now! Honestly, Poison types are going to be really good and in particular fantastic for punishing Ability-reliant Pokemon. Also, a question; does Poison Touch count for the "100% chance and Toxic"? Because Toxicroak Fake Outing into things is just evil at that point, if so.
Rubble: Never manually set Spikes again. Hazard management is going to be a must in Type Attributes.
Jagged: Very powerful, still able to remove 1/3rd of the enemie's HP in a single turn if they make contact with you and you make contact with them -and in fact multi-strike moves presumably trigger it on each hit, which gives us Fury Attack Rhyperior, Fury Swipes Barbaracle (Tough Claws boost, too. It also gets Dual Chop if you want to hit Ghosts) and Double Kick Terrakion. Fortunately, that's the entirety of Rock-type multi-strike-contact move stuff, so the possibility of removing 5/6ths of the enemy's HP in one move/all of it in one turn is fairly limited (There isn't even a Normal/Rock or a Rock/Ghost Pokemon to steal such a move), and Ghosts are immune to everything except Dual Chop, which is only two hits. That's not perfect, because Barbaracle and Rhyperior get Shadow Claw to punish Ghost type's, but it at least provides a reasonable possibility of an answer.
Tempered: Steel types are more obnoxiously bulky than ever. I'm assuming this applies to the Pokemon that is Steel type, and not just super-effective Fighting, Ground, and Fire moves?
Incinerator: For clarity, does the Knock Off comparison extend any further than "removes item, and not items that cannot be removed" ie does it get a 50% damage boost if it burns away the item? In any event, this helps the utility of a lot of Fire types that lack Knock Off, and can potentially help even the ones that have it since they can consider dumping Knock Off in favor of assuming their Fire STAB will get the job done. It especially makes stall-y Heatran obnoxious, since spamming Lava Plume is not only liable to Burn but also liable to wipe your item, all while getting in damage.
Purity: Does it clear Toxic Spikes only if the Pokemon is grounded, or does it clear Toxic Spikes period? Regardless, this makes bulky Water types amazing, since Toxic can't clear them out and they heal passively even if they aren't carrying Leftovers/you get rid of their Leftovers. Belly Drum Azumarill will actually be getting back HP each turn that passes! I'm especially interested in seeing how Alomomola performs in Type Attributes, since it gives it notable advantages over Chansey, reducing the degree to which it is "bad Water type Chansey". Also, is this literally the same thing as Aqua Ring (As in using Aqua Ring will fail, and it can be Baton Passed) or is it just a passive healing? The difference is pretty crucial.
Seedlings: Nothing will ever run Leech Seed again. (Well, maybe Smeargle, but I doubt it) This in particular makes Grass attacks a very safe move to use, bizarrely enough, since even something doubly resistant will hate being Super Seeded. Are Grass types immune to Super Seed just like they're immune to Leech Seed?
Capacitor: I alluded to this somewhat before, but this is a pretty notable effect. In particular, barring Battle Armor/Shell Armor (fffff Mega Slowbro being good in another OM) Electric types should never carry a Choice Band or a Choice Specs, because a Scope Lens will get the same boost on all their moves and punch straight through defensive boosts too. And it even ignores Unaware! Die Cosmic Power Clefable, die.
Manipulate: Very nice, though in practice it has the flaw that the moves Psychic types are weak to tend to have low BP (Knock Off in particular is hard hitting but has an actual BP of 65), so for a lot of Psychic types it isn't a good way to provide safe switch-ins. But there are exceptions -Metagross appreciates it because Earthquake or Fire Blast are so often the highest BP move on Pokemon carrying one of them.
Sub-Zero: Note that everything that resists Water is vulnerable to Sub-Zero Ice moves. Stallrein gets both Purity and this, and has perfect coverage offensively. (Well, almost perfect coverage -Thick Fat Walrein itself is resistant to both Water and Sub-Zero Ice) Stallrein is going to be ridiculously good, between excellent passive healing (Which it can supplement with Hail-backed Ice Body and Leftovers! 3/16th HP each turn while your enemy loses 1/16th? Yes please) Cloyster is another noteworthy, since a Shell Smash run isn't slowed down at all by switching in a Water type. And OK yeah Lapras and Dewgong benefit too whatever. (To be fair, stall Lapras is pretty plausible) Also, is "this Pokemon takes not-very-effective damage from Fire attacks" merely a poor framing, or do you in fact mean that being Ice type alters the Fire interaction to always be singly ineffective even if it should be neutral or double ineffective?
Legendary Entrance: To clarify; does the Twister behave exactly as actual Twister, ie ineffective against Steel, super effective against Dragons, useless against Fairies, capable of hitting Pokemon that are mid-air and doing doubled damage in the process, and getting STAB because the user is of course a Dragon type? Or do you mean "40 BP attack"? For that matter, from a Doubles/Triples perspective, does it spread? Regardless, this is a great way to break Sashes, Subs, Sturdy, and Multiscale (You know, other than the fact that Dragonite will probably just kill you with Dragon Claw/Outrage/Draco Meteor), finish off weakened opponents without giving them a chance at even an increased priority move move ("[name] held on with its Focus Sash! Dragonite switched in, its Legendary Entrance stirred up a Twister! [name] fainted!"), and just general chipping damage for absolutely free. Thank goodness there's no Dragon type Regenerator -that would just be heinous.
Dirty Tricks: Again, clarification; is this in every respect identical to Taunt, or is it a pseudo-Taunt in the same way that Intimidate is a Growl, only for instance Magic Bounce will reflect Growl but not Intimidate? If it's a true Intimidate-Taunt, say hello to the death of Stall, gg, everybody take their Chansey and go home. If it can be blocked by Magic Bounce, that helps, though it's still an enormous hit to stall. Regardless, very very very influential, arguably more distorting than Stealth Rocks in Standard.
Benevolent: Regenerator Wish Core! Wigglytuff, Aromatisse, Azumarill, and in Ubers Xerneas are by far the most notable Fairies regarding this effect, with a minor round of applause for Mega Audino (But really it's just crappy Wigglytuff), since no other Fairy breaks reaches 100 HP. Even so, free weak-Wishing when you're switching Sylveon, Mega Gardevoir, etc is still pretty good, especially since unlike an actual Wish it isn't blatantly telegraphed a turn ahead of time. A question though; does it stack with an actual Wish, or does the Wish override Benevolent's pseudo-Wish?