Can you have genetic testing done by urine testing?

Yes. Some conditions like the organic acidurias are best tested in urine.
Hard to say. You get more from this site when you provide background info on a problem and ask a related question. Blind questions are often too vague to answer. We can do a lot of things to any cells we might find in or on any substance. If your concern is identifying paternity, chromosome problems, inherited diseases, etc, you should say so. You are welcome to start over. Posts are not linked.
Yes. Many inborn errors of metabolism can be identified through substances excreted in the urine. Urine tests can also be used to detect DNA particles of some infections and some cancers.