You can apply for two cards almost simultaneously by completing each application in a separate browser window, and submitting them within a few seconds. However, Citi will do a separate inquiry for each application. It is the credit bureau that decides to combine the inquiries because they might be duplicates. There is no guarantee that Citi will use the same bureau for both applications, nor any guarantee that the bureau will see them as duplicates.

Small business cards are issued to individuals, not to companies. It doesn't matter how old your LLC is, the issuer will check your personal credit and you will be personally responsible for the debt.