Scarlett,
What do you know about Russian? Something about the cases, how to decline the verbs etc? Any simple textbook contains answers on your questions.
Говоришь is the other form of the verb "говорить" (infinitive).
singular:
Я говорю. (I speak)
Ты говоришь. (Thou speak)
Он/она/оно говорит. (He/she/it speaks)
plural:
Мы говорим. (We speak)
Вы говорите. (You speak)
Они говорят. (They speak)

All of the verbs above mean "говорить", but they are in different forms. If you want to ask "do you speak ...?" in Russian, you should select a form of the verb depending on a person (persons) you're addressing or asking about.

But "ты говоришь по-русски?" sounds like "you speak Russian?".
If you see the mark "?" at the end of a sentence, it implies question. So the right answer is "Do you speak Russian?"
"You speak Russian" = "Ты говоришь по-русски" (without "?", it's an affirmative sentence).

When we use the verb "can" in Russian, we must use infinitives (as you know it's incorrect in English). So, if you use "могу/можешь" and so on, you should put an infinitive after it.