Perjury is the legal definition for lying under oath (anywhere)
absolutely not
i can administer 10 oaths of truthfulness to you and have you sign 10 attestations that you didnt borrow my pen, and have all this witnessed, and when you admit you borrowed my pen you cannot be prosecuted for perjury. government invasiveness has not yet reached such as a ridiculous level as applying perjury to 2 private parties. whether individuals or an private businesses.
fraud? it depends, but perjury? no