Will iCal push an ABnB reservation it downloaded and push it to VRBO?

If I get a new reservation downloaded to OR through an ABnB iCal link will OR push that up to VRBO if I have iCal going both ways for both VRBO and ABnB?

Yes, as a block. OwnerRez won't push detailed information about your guest out to any of the channels, of course, but it will make sure the calendar is blocked for the booking time.

I have my first booking from airbnb. Do I have to send out all emails for the contract etc manually?

You can set up OwnerRez to do that for you automatically. You do have to do the initial setup though.

https://www.ownerrez.com/support/articles/airbnb-request-for-contact-info-real-email-address-and-signed-renter-agreement