Thanks for the compliment! Please find my answers to your questions below:
1. You enter the outgoing server information from the imap settings in Zoho when you are setting up your business email to send through gmail. See the 4th image from the top above, where it says “smtp server”.
2. By default emails sent to your business email address should not skip your inbox. When you created the filter did you select “skip inbox” by mistake?
Hope that helps. Let me know if you have any other questions.