How does Checkout affect existing processes, such as lead management, Trialforce, and trial licenses? For example, how will Checkout signup interact with lead processing?

Checkout doesn’t affect the way leads are sent to you, nor does it affect Trialforce configuration. However, it does change the way AppExchange trial licenses are managed. When a customer signs up for a trial using Checkout, the checkout trial user is listed as Active in the LMA.