Learn Spanish (Spain): Hoy he defendido mis derechos.

In Spain, you use the present perfect when the time period isn't over yet. Because the sentence uses hoy (today), the time frame is still open, so you must use he defendido. If the action happened yesterday (ayer), you would use the simple past: ayer defendí.

Doesn't derecho usually mean "straight" or the direction "right"?

Yes, it does! However, when used as a noun, un derecho means a legal or moral "right". It can also refer to the study of law. Here, mis derechos simply translates to "my rights".

Defender changes to defiendo in the present tense. Why isn't there a stem change in defendido?

While defender is a stem-changing verb in the present tense (the "e" becomes "ie"), stem changes do not apply to the past participles of regular -er verbs. You just drop the -er and add -ido to make defendido.

Why is the word mis plural when only one person is defending their rights?

In Spanish, possessive adjectives like mi (my) must match the noun they belong to, not the owner. Because derechos is plural, the word describing it must also be plural, becoming mis.