Ce weekend le, vendredi (soir), j'avais finalemente fini le travaille, et j'ai rejoignant maon amie, Brooke, pour le dîner.

"rejoignant" is the present participle, "rejoint" the past one
Feminine nouns starting with a vowel (like "amie") are treated like masculine nouns when it comes to articles and possessive pronouns. The reason is purely euphonic: it's meant to avoid having two vowels following each other, which would be the case in *ma amie

Elle avait aussi fini le travaille.

Past action (finir le travail) from a past perspective (when you were dining out) => plus-que-parfait

Le jour prochain, j'ai marchsuivant, je me suis promené dans le parc et j'ai appelé ma mère pour parler/discuter.

"prochain" only applies from the perspective of a speaker talking in a particular time. It's like "today", you can't use it if you refer to anything else as the very day you're talking from

"marcher" insists on the way the movement is done. If you just mean you had a stroll, "je me suis baladé/promené" or "j'ai fait un tour au parc" are way better

Elle a voyagé à New York avec son petit- ami à New York pourpour rendre visiter à ses cousins.

"visiter" is mostly said for sick/ill people. The neutral term is "rendre visite à"

Le dimanche, j'ai fait lde l'exercice, et j'ai lu et fait mes devoirs de la classe de français.

"devoirs de français" is enough for "French homework"
If you meant you worked out, "exercice" is always considered uncountable, so it's always "faire DE l'exercice"