"This is a new moment, a new reality."
Translation:Este é um novo momento, uma nova realidade.
You could use in conversation. But isso/isto/aquilo are neutral and cant be used with the object. So, este (for masculine words) is the best option once we have the object. (Moment)
Why do the adjectives here come before the nouns they describe? When do they come after the noun?
They generally come after the noun in Portuguese, knowing when they can come before the noun takes practice and trial and error. It depends on the noun and it depends on the adjective.
The adjective's position can also modify the meaning of the sentence, for example "Um grande homem" does not mean the same thing as "Um homem grande". The first means "A big man", the second means "A great man"