There’s nothing awkward about studying. On the contrary, I’d be impressed if I noticed someone doing that. Anyway, you don’t need to shout out your sentences in public. Speaking softly is enough, even without opening your mouth. But do pronounce everything you hear!
Is it okay to read the text while repeating or better not to?
Personally, I rely on text as little as possible. Reading while mimicking is like riding a bicycle with a 3rd wheel. Resist the temptation to