How's Katarina right now in terms of balance? Is she being looked at?
Katarina is really...weird. When shes strong, both in the overall meta and in a particular game, she feels stronger than like any other champion(at least in yolo queue). And vice versa. In the past, before her repeated nerfs in late s4/ early s5, she terrorized solo queue and was nearly perma-banned. And in game she actually had a strong laning phase with her high sustain 4 pot start and high base damages early. She'd often win lanes around levels 5-7 when her Q poke and superior effective HP with potions would allow her to whittle down opponents and force them out of lane/kill them. And if she got ahead early, or got some kills in a skrimish, she'd snowball the game out of control, because a fed Katarina could duel any squishy and even win 1 vs 2/3s, with little counterplay unless you had point and click hard cc(which isn't enough if she's sufficiently ahead). Present day Katarina can do the same thing if she gets snowballed, but her laning phase is only describable as terrible. IIRC she has the 2nd lowest base health regen after Riven, and her base health was nerfed at some point too. Coupled with base damage nerfs on her E and R and she has lost her ability to trade effectively without her ultimate and lost her ability to sustain through poke. My point is present state Katarina feels really really weak in lane (and by extension weak later if she didn't find a way to snowball) but really really strong if she does get that early lead, and she still retains the ability to instantly annihilate groups of squishies with items. She's very black and white in terms of power, and I think her identity as a champion should lie more in her cleanup and opportunistic nature than in simply snowballing and exploding everyone.
I think Katarina needs to move away from the overbearing snowball playstyle and be more clearly defined as a clean-up champion. I don't really know how to accomplish this but if I had to try I'd say maybe give her better ratio on her W(.25 to .35ish) and maybe some base damage (like 5 per rank, so 25 extra at lvl 5?, but reduce the ludicrous .25 AP ratio per dagger on her ultimate (2.5 overall) to some thing like .2 per dagger? This would give her less insta-gib potential but a safer lane and a bit more damage with resets. And I think she deserves her base health regen back(but keep the flat health nerfs). All these DoT mages that are really strong with the new mastery are dumping on Kat in lane even with her 4 pot start. If it turns out these changes made her laning phase too strong again then maybe the initial Q damage could be lowered but the proc damage increased, to prevent her from Q spamming as harass.
Another idea I have is adding another part to her passive, where if she gets a kill/assist in 3 seconds she gets a bonus % increase in her damage, or bonus magic penetration. (if this were implemented then her numbers would probably have to be tuned again.) Or something else entirely.