Learn Spanish (Latin America): Yo escribo porque quiero aprender.

When written as one word without an accent, porque means because, which we use to give a reason. If you see it written as two words with an accent mark (por qué), it means why and is used to ask questions.

Why is the second verb aprender left in its basic form instead of being conjugated?

When two verbs are used right next to each other to express a single idea, only the first one gets changed (conjugated) to match the person doing the action. Here, quiero is changed to mean I want, so the second verb aprender (to learn) stays in its basic dictionary form, which is called the infinitive.

There is a yo at the beginning, but why isn't there another yo before quiero?

In Spanish, you do not need to repeat the subject pronoun if it is already clear. The verb quiero always means I want, and since we just established who is talking in the first part of the sentence, we can safely leave out the second yo.

Could I drop the first yo as well and just say Escribo porque quiero aprender?

Yes, absolutely! The ending of escribo already tells us that I am the one writing, so the yo is completely optional. Including it here just adds a little bit of focus or emphasis on the speaker.