some of these are quite easily explainable.
Why is Anivia, a creature that flies one of the slowest moving champions in the game?
Either she's just being chill and could move faster if she wanted (This fits her personality but is kinda eh). OR She has to spend most of her energy keeping herself afloat, and as such can't really push herself forward all that fast.
Why is it that buying a long sword when i use a ranged champion such as Vayne increase my damage?
It's just a magic charm that augments your character. Vayne would just shove a little long sword shaped trinket in her pocket and move on.