Can all these screenings cause unnecessary stresses on the newborn?

Define unnecessary. I worked at a Child Development Center where we say children who had metabolic problems like unrecognized PKU, hypothroidism, and even rarer conditions. None of their parents were happy to hear the kid would be brain injured for the rest of their life from a condition that could have been prevented by early screening.Just because you think your kid could never have the problem doesn't make it true.
Unlikely. Screenings which occur in the newborn period include a hearing test, a metabolic blood screen, a screen for jaundice, and occasionally an oxygen level check. Except for the blood test, all of the others are painless. They are all intended to see if the baby was born with a treatable condition which could cause a severe disability or death. Some of these are otherwise unnoticed in newborns.
Probably not. The screenings that are done on newborns are meant to identify rare and deadly metabolic problems or hearing issues that can lead to developmental problems. When you weigh the risks and benefits of doing the tests vs not doing them, i think most parents will say they are worth it.