Quote Originally Posted by Scarlett View Post
Thank you.

But "ты говоришь по-русски?" sounds like "you speak Russian?". Does that mean it's unnecessary/unnatural to include "can" (можешь)?
Yes, it sounds like that but when you ask "ты говоришь по-русски" all you want to know if the person you're talking to is able to speak Russian. If you add можешь to your question it still sounds like you want to know if the person speaks Russian. So можешь is redundant there. You don't need to use that word to get the point across.

Quote Originally Posted by Scarlett View Post
Also, is there a significant difference between "говоришь" and "говорить", do they have to be used in certain context, or are they interchangeable?
This is the matter of basic grammar. Говорить is the infinitive form of the verb, говоришь is the second person singular and present tense declension of the verb, говорите is the second person plural and present tense declension of the verb.