Your assumptions are mostly correct.
Ese means "that", and as you said it is masculine. It can be used as an adjective and also as a noun.
Ese día = that day. (demonstrative adjective)
Ese auto = that car. (demonstrative adjective)
Ese es más grande = that one is bigger. (demonstrative noun)
Eso also means "that". The main difference is that "eso" can only be used as a noun, never as an adjective. You cannot say "eso auto". "Eso" should always be the subject performing the action.
Eso es bueno = that is good.
Eso tiene muchas caracterísiticas positivas = that has a lot of positive features.
Esa is the feminine of "eso" and it can be used as a noun ans as an adjective.
Esa casa es grande = that house is big. (demonstrative adjective)
Esa idea me gusta = I like that idea. (demonstrative adjective).
Esa es mejor = that one is better (demonstrative noun).
Additional information, the counterparts of "ese, eso, esa" meaning "that" are "este, esto, esta", meaning "this". "Este" and "esta" may be used as nouns or adjectives, just as "ese" and "esa". "Esto" may only be used as a noun, just as "eso".
I hope this answers your question.