Lex Corp and Alva Industries are business partners.
Both of them seem to be mega corporations involved in creating advanced and futuristic technology, and they both happen to be run by rather unscrupulous businessmen; although Lex Luthor is far more evil than Edwin Alva, who just seems to be a bit amoral. It would make sense that these two companies are sharing some resources with each other. Kara and Clark are still biological cousins.
Argo and Krypton were both technologically advanced neighboring planets. It isn't inconceivable that there was some travel between them. Lara Sul-Van could have had a brother who immigrated to Argo and married Kara's mother. Toyman's father wasn't framed, he really was guilty.
Winslow Schott Jr. AKA "The Toyman" says his father was framed for Bruno Manheim's crimes, but the newspaper article Clark finds at the Daily Planet says that a numbers business was being run out of his toy factory. Even if he wasn't running the racket personally, it's very hard to believe that Winslow Sr. had no idea what was going on, but was happy to accept Manheim's money anyway. At the very least, it makes him an accomplice or accessory. In the end though, Toyman was still bussed around foster homes, so his childhood was ruined either way. Not surprising he still tries to think the best of his father. But since Toyman is a Psychotic Manchild, he may also be an Unreliable Narrator.- The Episode itself actually hints at this. Toyman says that Manheim offered to fund the factory "under one condition". It can be assumed that the "condition" was that he let Manheim run the racket from the factory. So he did know, but Toyman could still feel that his dad was pressed into it.
