Learn Russian: Вы можете петь тихо?

Just like in English, when you use a modal verb like можете (can), the main action verb that follows it stays in the infinitive (the dictionary form). Because можете is already conjugated to match Вы, петь (to sing) doesn't change.

The verb for 'can' is мочь, so why does it look so different here as можете?

Мочь (to be able to) has a slightly irregular conjugation pattern where the stem consonant changes. Because the subject is Вы (you, formal or plural), we must use the matching form можете. You might also remember the form for 'I can', which is я могу.

There is no flipped word order or helper word like 'Do'. How do we know this is a question?

In Russian, you don't need to change the word order to ask a simple yes/no question. The statement 'You can sing quietly' and the question 'Can you sing quietly?' use the exact same words: Вы можете петь тихо. You simply add a question mark in writing, and raise the pitch of your voice when speaking.

Would the word тихо (quietly) change its ending if we used a different subject, like она (she)?

No, it will always stay exactly as тихо. It is an adverb, which means it describes how an action is done. Unlike adjectives, adverbs in Russian never change their endings to match gender or number.