In Italian do all adjectives change their endings depending on the plurality and gender of the noun?
Short answer: no.
All adjectives are always set to the same gender and number as the noun they refer to, but the endings vary and sometimes there's no change: for instance grande/grandi (no change with gender).
There are two classes of adjectives in Italian and the only way to tell which one each belongs to is to look at their base form: if it ends in -o (e.g. annoiato, annoyed) then it belongs to the first one, otherwise if it ends in -e (e.g. felice = happy) it will belong to the second one. When I say the base form, I mean the one you would use to look up the meaning of the word in a dictionary. Though annoiate does exist, it's the form you would use in 'the women are annoyed'='le donne sono annoiate'; but it is not its base form. Hope I didn't overcomplicate things.