I think putting AD on dianas Q would help her put out more damage, i mean she can do damage now but I personally don't think diana is as strong as she truly could be.
How would that help her do more damage?
Rabadon's AP bonus scales with AP, Lich Bane's burst only scales with AP, and Gunblade doesn't contribute to damage so much as it gives a cool active and sustain.
Also - just as Rabadon and Lich Bane don't scale with AD, AP itself doesn't scale with Crit, AS, Armor penetration, life steal, Hydra/Hurricane AoE, etc.
Getting 80 AD + 120 AP doesn't give you more damage than 80 AD + 80 AD or 120 AP + 120 AP, the damage of 80 AD + 120 AP is pretty much exactly the same.
And then the 160 AD or 240 AP guy gets something like IE, Rabadon's, Statik Shiv, Lich Bane, Last Whisper or Void Staff and they tend to get another ~160 AD/~240 AP spike on top of that, where with hybrid items you're looking at either 80 AD or 120 AP (or something like 40 AD+60 AP)
Adding an AD ratio would not allow Diana to do more damage. It would just make her like Akali or Katarina - completly indiferent to the fact she has an AD ratio, because it does nothing for her end-game scalings.
The only useful thing with split AD/AP ratios in a kit is when those kits do a mixture of physical/magical damage that basically says "you can't counter-build me in lane ever and I basically have a free Last Whisper/Void Staff if you try building MR or Armor against me". Extremely useful early, very useful mid-game, questionably useful late when you could exceed that bonus with actually having Last Whisper or Void Staff with other forms of penetration (still pretty useful end-game if you're a tank and actually need to focus on building tank items).
Her E does no damage at all. I think they should do something to her to help her do more damage. i'm not saying make her broken just stronger.
Abilities aren't created in a void, they're made in tandem with a champion's kit. Riot is well aware things like Yasou's Steel Tempest allow him to cast his ultimate.
Same deal with Diana - typical champion gains ~40 ability damage per level and ends with ~1000 QWER damage @18.
Diana has 1100 damage in her QWER rotation, provided she unleashes 1 AA for her passive and casts her ult twice via the moonlight reset.
Which, for all intents and purposes, tends to mean having a no-damage ability actually gives you more damage, because you can max out your base damage in the QWE portion significantly earlier.
In several cases it also means you only need to cast 3 abilities rather than 4, though Diana still needs to double-cast and land an AA, so she doesn't get that benefit of having her burst crammed into 3 skills rather than spread out over 4.
Anyways - you're ideas, when implemented properly in a balanced fashion, would actually cause Diana to do less damage rather than more damage.