No, it will not because they do not test for it. It's a non-narcotic pain reliever. They only test for controlled substances and narcotics like THC (found in marijuana), cocaine, opiates (heroin and...
Yes, alcohol can show up in a urine screen. Some tests can go as far back as eighty hours. Those tests are usually for zero tolerance rules for companies, courts, etc.
Fentanyl will show up as fentanyl but this is almost never tested for. It is a special test which is also expensive and I would only suspect it being tested for if one had access to it, i.e....