Can you have lupus without any sort of rashes? Does it cause. Utis?

While there are. Characteristic rashes in sle, this is not required for diagnosis. Utis are not associated.
Yes. Lupus is a systemic diseases , can affect various organs. Rash is usually early symptom, but not always. UTI is not always a common manifestation, however urine analysis can have abnormalities which may look like UTI. Lupus affects kidney and can cause abnormalities in urine analysis.
Yes. Lupus can present itself with several clinical manifestations: rash, joint pains, non specific fatigue, myalgias, etc., etc. While all these clinical symptoms give some clue for further investigation; none of these is a ' must have' for making the diagnosis. The definitive diagnosis is made through serology.