Learn German: Die Ärztinnen sprechen Deutsch. - The doctors female speak German.

This is the plural form for female doctors. The word for a male doctor is Arzt. To make it female, German adds -in and an umlaut to get Ärztin. When making a feminine noun ending in -in plural, you always double the "n" and add -en, giving us Ärztinnen.

Is sprechen a regular verb? I thought it changed to spricht.

sprechen (to speak) is an irregular verb, but the vowel change only happens in the singular forms for "you" (du sprichst) and "he/she/it" (er/sie/es spricht). For plural subjects like "they" (the doctors), it goes back to the regular -e- and is conjugated normally as sprechen.

Why is Deutsch capitalized here?

In German, every single noun must be capitalized. Because Deutsch (German) is the name of a language, it acts as a noun in this sentence and gets a capital letter.

Does die here mean "the" (feminine) or "the" (plural)?

Here, die means "the" in the plural. Although the word for a single female doctor also uses die (die Ärztin), we know this sentence is plural because of the plural noun Ärztinnen and the plural verb ending in -en (sprechen).