When they test for utis do they test for everything?

Not everything, but: Routine urine dipstick tests for utis, also sugar in urine which can lead to diagnosis of diabetes, tests for protein which could reveal non-uti kidney disease, urinary specific gravity (concentration), ph (urinary acidity), ketones (+ve for starvation or not having eaten for a while, blood can be +ve for uti, kidney disease or cancer, bilirubin for jaundice or liver disease.
No. Anytime tests are done, only the tests the doctor orders are done. If you had a test for a UTI and you are worried you have something else (like pregnancy or a sexually transmitted disease for instance), then you should go back and get tested again.