I'm kinda unsure how the passive works. You say it applies stack of Hunter's Mark then say at 5 stacks of Hunter's Mark the enemy will recieve the Hunter's mark. Its a little confusing, you need to clear this up. I think if you wanted to keep it somewhat like it is, it either needs to be something like Caitlyn's or a reverse Lux ability. Either have it charge up and on every 5th attack you make it applies the mark or attacking an enemy first makes your abilities have extra effects on them. Might be better to just come up with something else tho, right now its kinda boring. Maybe stacks that increased your damage against that enemy when you hit them repeatedly might work better. Something like "Each attack applies Hunter's Mark and Red gains increased damage against her prey. Red gains 5% Armor Pen per stack against marked target and gains 5% MS per stack if moving towards her target, maximum of 5 stacks per target, stacks last 5 seconds." This would show off her hunter's side of things, the whole thrill of the hunt and stuff. I would have the stacks not get reset if she attacks another enemy.
The passive on Q doesn't need the damage bonus. It would be way to powerful for her basic attacks to apply a mark and then every attack on that enemy after it deals that much bonus damage. The AS and mana regen on it is okay.
The active needs work and some clarification. Is this a skill shot? Is it targeted? It seems like this is her farming ability, shoot it thru a minion wave, apply some marks, and deal some damage, but its unclear. I could just be reading it wrong and its a long range shot that only hits one enemy for some damage. Its a little underwhelming currently both ways. As a farming tool it doesn't seem like it would have a wide enough AoE to help hit waves that are already there like Cait's Q can do, so this would have to be about the width of a single TF card flying in the direction you sent it and if thats the case the damage seems a little low. It needs a range and damage increase overall. Range needs to go up to something more like 1200 and the base damage needs to be increased greatly. 70 is a good starting point, but the base damage should be topping off 200 - 250. Your ratio on it is okay and the thing about hitting one of your marked targets needs to scale. Something like 20/40/60/80/100 then an additional 20 damage or so per stack above 1. This will give you a better sense of reward for getting 5 stacks on someone and then hitting them with this without it being too overpowered. As far as applying marks does it just apply marks to the last enemy hit or each enemy hit with the last one getting 3 total. Work on the wording of this ability.
On the W, i think all of your traps need to deal some damage to whoever tripped them. On this one, maybe lets it cause the target to bleed for a bit if they have been marked by you based on how many stacks they have. Also does this have a set up time like Caitlyn's trap or does it activate the instant you drop it. The stun trap is okay. The slow trap needs to be more defined. Does this only slow the person hit or does this release an AoE cloud. If it only effects the person hit the slow needs to be increased greatly, like up to 50%, if its an AoE it needs to be increased up to 25% or 30%. The damaging trap needs its damage increased.
The E is pretty good overall, the passive is okay. The active is fine tho again I would increase the slow amount on this one to around 20% - 25% and give it some damage. Also needs a mana cost for summoning Grey.
Need to redo the R. Its pretty much a ****tier Vayne Ult. The passive on it works. If you're wanting to give her a steriod for her ult, make it a good one. Not just barely increased move speed while stealthed for a few second then barely any extra damage after stealth is broken. Look at Twitch's Ult, around the same duration but you get **** tons more damage from his then you do from this due to it being a base attack increase along with piercing shots. Then check out Vayne's 90 MS when moving toward an enemy champ, stealth when she tumbles, and increased damage. If you are going to keep it with percentages (personally I like using them, some people prefer base increases) have it give her 15/20/25% more AD, MS, and AS for both her and the wolf for a few seconds along with maybe giving her an extra on hit effect with some of her abilities. Either slightly increased damage, a bleed or slow or something else.
I like your idea. I think League needs a pet champ because Yorick's ghost don't last long enough for me to really consider them pets, Tibbers is a short duration Ult, and you can't control Malzahar's pets. Good work