Is that a good idea or no. like. ok im a noob lat and i still hardly know how to build her but i always get 
first. but last night while i practiced in a custom i got 
and kat went ballistic and i just crushed after that. so i was thinking. would it be a good idea to get that for her in early game, or even in general?
Katarina doesnt benefit from the AS or from the passive. So she really only gets the 20% cdr and 60 AP. It is not very gold efficient at all. (You'd be better off getting a Morello's than it and she doesn't even need the Mana regen)
would be my ideal build on her. You have the Armor and M.resist on GA, Zhonya's, and Abyssal + they all give additional things you want (Zhonya's active + 120 AP, Abyssal AP + Reducing enemy MR, GA gives a revive that could let your CD's come up for you to either get more kills or escape.)
Against an AP midlaner I would go Abyssal > Rabadons > Voidstaff > Zhonya Against an AD midlaner I would go Zhonya > Rabadons > Voidstaff > Abyssal
I can see the attraction of Hextech Gunblade though, I might pick that up over the Abyssal some games (if they aren't building any M.Resist for example)
Not to tell you what to do, and honestly, if you're doing what you're comfortable with, you can make any combination of items work, but Katarina tends to benefit most from an AP heavy build.
Tends to, doesn't mean it's the only way to build her. With the AS boost, Nashor's Tooth is an AP Item for Auto-Attack heavy champs, which, in general, Katarina really isn't. She's a burst Assassin who wants to Shunpo in, spill out the rest of her kit with few to no auto-attacks, and shunpo back out after securing the kill.
She does well with:
Zhonya's Hourglass
Rabadon's Deathcap
Abyssal Sceptre
The HP from 
Rod of Ages can help late game (Also the late game AP), but it's build path is mostly unhelpful to the manaless katarina.
i mean its an interesting item choice but i would probably never build it on her and i don't see it being built on her. only way i could see it being semi decent would be if your ult or any of your abilities apply on hit effects
Those items aren't BAD for Kat necessarily, it's more that when you're spending that kind of gold there are others that are far, far more useful for her. Zhonya's is a good item to build first because as soon as you have Seeker's Armguard it gives you some armor. This is especially useful if the enemy midlaner has abilities that do physical damage, as noted above, but it's also good just to reduce the damage you take from ranged basic attacks and minions. Rabadon's might be worth an all-out rush if the situation allows, but definitely not Gunblade.
Once you have Sorceror's Shoes, Rabadon's, and Zhonya's, probably the next best projects are Abyssal Scepter, Void Staff, or Rylai's (sad that Deathfire Grasp is no more...)
It may not be a bad idea to pick up Haunting Guise early on. You can build it easily out of amplifying tome + ruby crystal, both of which are helpful early and the magic penetration is great to have once you've built Zhonya's and/or Rabadon's. DON'T build Liandry's, though. Not worth. Sell Haunting Guise to make room for other items when you need to.
Is that a good idea or no. like. ok im a noob lat and i still hardly know how to build her but i always get
The biggest issue with building nashor's tooth on katarina is the fact that she has a small attack range and does not get to autoattack the enemy very often so the item isn't very efficient for her playstyle. If you're interested in building cooldown reduction on her , i recommend picking up a fiendish codex since it can be built into certain items.
