ALL of her attacks are GOD awful slow.
Q and E ez to dodge with all the mobility of anyone after S6
W is blocked/countered by everything and that is her main source of damage.
Her auto attacks and W are so slow Soraka's Bananas hit first.
Any auto attack melee can walk around her and out trade her without boots.
Any CC counters her 100%
She need a full rework to bring her into the new meta of champs.
TitanAnteus2 votesPeople are learning how to play against her.
...
Ok after reading your entire post it's more like you just need advice to up your illaoi game.
Here's some advice. It is much easier to land your E if the enemy is farming. The game has become unforgiven. Champions missing abilities is seriously going to hurt you. This is the same for every champion from Zoe to Caitlyn. DO NOT MISS IT!
Yes her Autos are slow. This is because they are not the main source of her damage. She's basically a juggernaut. Don't seriously aim for kills. Just like Shen just exploit enemy openings. Build Health and get the tower destruction rune and you'll be a HUGE asset to your team.
Some more general advice, that you might already know about.
When you Q, try to hit both the ghost and the enemy champion. Try not to ult until you have two tentacles around you. The extra tentacles that spawn will increase the damage by A LOT. Also, ULT in locations where the enemy champion is forced to deal with you. Ulting around objectives like a turret that's about to go down, or dragon or baron are your best bet. They'll be forced to deal with you, and dealing with illaoi under her tentacles is suicide.
She has a lot of nuance as a champion and I know that her weaknesses seem glaring at first, but once you get used to her she's quite strong.
