I don't know how you learn Japanese grammar but as a Japanese speaker,
I will explain what I thought.
You can think suffix 性 is 性 as in 性質, meaning character/quality.
When you say 論理性, it means how much something has character/quality of
論理 (logic), meaning how logical something is.
経済性 how economical something is
現実性 how realistic something is
論理性 how logiacal something is
危険性 how dangerous something is
関連性 how relevant something is to ---
規則性 how regular/how much regurality some thing has
安全性 how safe something is
>Is 高さ also an abstract noun?
Yeah, I think so.
>If so does that mean さ is basically 性?
さ is something that change adjective to noun.