You should do what your vet is suggesting as long as they are moving ahead and trying to find an answer. If they want to send urine for culture, then yes, it should be a sterile sample. Not sure why they would rerun a u/a at this point.
A cysto does not need to be u/s guided if your vet is fine doing it another way. With Ellie, it usually is because her bladder is hard to find. There is a slight risk, but there is even a slight risk for drawing blood, esp. from the jugular, so just trust that your vet has done this many times before and will do fine. I've even watched the procedure before. The pups really do not care what is being done to them in most cases.