Is it illegal to say something that is not true about a website's history or background? Such as, "Edsenty's are handpicked products by a chef in LA"

Not all misstetements used to sell products or services would violate consumer protection laws, becasue some may be so minor or so obvious as to constitute "mere puffery", but in general misstatements of fact used to induce people to buy your product or service would violate those laws.  I think your example would be a violation.