They'll need to do a urinalysis to diagnose an URI. Typically they will do a procedure called a cystocentesis, which is where they collect urine directly from the bladder. Do not worry! It is safe and painless! We are currently treating a URI and thats actually how my guy was diagnosed with diabetes!
A sharp decline in water intake could cause a URI or irritation of the bladder due to more concentrate urine. Though, if you are feeding wet food, cats will get the majority of their water from their food. I blend my wet food with a little bit of water to make a paste like consistency. It encourages more liquid intake and helps Poopy eat because hes down to only his front canines left!
Crystals/stones form in the bladder for a few different reasons. Treatment is based on the cause of the stones, and they can diagnose the stones with a urinalysis too. I am not familiar enough with stones to be able to be of much help there.
Keep us updated, hope its something easily treatable! <3