In a palace of formations, my mother was my powerhouse and father a school of thoughts.
Is this style of writing correct? What can be better choice for the same sentence, grammatically?
Your use of metaphors is correct and used often.
My mother is my powerhouse.
is understandable and correct, however the same notion is usually expressed as
My mother is my strength.
Your second phrase
father a school of thought (singular)
has the meaning one has created a school of thought
it is along the same lines of the idiom
every great idea has a thousand fathers.
meaning if there is a great idea, many people will want to claim credit for it.