Por fin termino mi tarea y descanso un poco.

por fin means finally or at last and is very common in everyday speech to express relief or satisfaction that something has happened.
finalmente is a direct synonym but sounds slightly more formal or neutral.
al fin also means at last but is less common in Latin America and can feel more literary or formal.

Spanish can use the simple present (termino) to describe an action that has just finished or that you’re experiencing now, giving a sense of immediacy (like “I just finish my homework”).
If you prefer a clear past narration, you would say Por fin terminé mi tarea y descansé un poco, using the preterite.

No accent is needed on termino because it’s the first-person singular ending in –o of the present indicative (yo termino).
terminó (with an accent) is the third-person singular in the preterite (él/ella/usted terminó) meaning “he/she/you (formal) finished.”

Spanish is a pro-drop language, so you drop the subject pronoun when the verb ending already tells you who the subject is.
Adding yo (Por fin yo termino mi tarea) is possible for extra emphasis but normally it’s omitted.

The verb descansar is intransitive and doesn’t require a reflexive pronoun, so descanso un poco (“I rest a bit”) is standard.
Using me descanso is grammatically acceptable but redundant in everyday speech—it just adds an unnecessary “myself” emphasis.

descanso un poco means “I rest a little” or “I take a short break.”
If you say descanso poco, it changes to “I don’t rest much,” giving a negative nuance (you rest very little).

Yes. terminar + noun (termino mi tarea) treats “homework” as a thing you finish.
terminar de + infinitive (termino de hacer mi tarea) emphasizes completing the action of doing homework. Use terminar de when the focus is on finishing an activity rather than a physical object.