How to send messages between AWS VPCs?

Question

I'm trying to understand how to send integration messages between applications. In the following scenario:

1. User in Application 1 generates a query.
2. That query gets sent to Application 2
3. Application 2 returns the results and sends it back to Application 1

My specific questions are the following:

1. Does Application 1 need to do anything related to the On-Premise Application, or is that all the responsibility of the infrastructure of `AWS VPC 2' to figure out once receiving a request?
2. Once an AWS PrivateLink is established, is it just a matter of sending messages back-and-forth between the 2 AWS VPC addresses? If so, how do you send messages to these addresses?