Do words in Portuguese inflect based upon case/time/gender/etc.? If so, how which parts of speech inflect?

Answer 1

In short. Yes.

Both Portuguese  and Spanish both are so similar and have gendered nouns of masculine or feminine words. Unlike its mother language Latin, they have no neuter gender. In both languages, feminine nouns often end in -a while masculine nouns often end in -o.

with adjectives, in both languages they must match the subject noun in gender and number (plural/singular )