Learn German: Er spricht Deutsch, Englisch und so weiter. - He speaks German, English and so on.

In German, names of languages are treated as nouns, so they must be capitalized. They are only lowercased when used as adjectives, such as describing a German city.

Why isn't there an article before the languages, like das Deutsch?

When you talk about speaking, learning, or understanding a general language, you drop the article in German. You only use the article when describing the language specifically, like das Deutsch, das er spricht (the German that he speaks).

Is there a common abbreviation for und so weiter like we use etc. in English?

Yes! In written German, you will very often see usw. which stands for und so weiter. It is used exactly like etc. in English.

I remember sprechen has a vowel change. Is it only for er?

sprechen is a strong verb that changes its stem vowel from e to i in the present tense for both the second and third person singular. So you get du sprichst and er spricht, but the rest of the forms keep the e, like wir sprechen.