Is it possible to propagate a list to a variation site by powershell?
No, it's only possible using the UI
I have been looking for a solution; but it seems this is not possible programmatically. You'll find workarounds where you have to create event listeners and sync the list yourself as jaloplo mentioned.
Yes, it is possible but not in a simple way. I made some powershell scripts that configures the lists (configure moderation an versioning, adds some properties to the root folder, adds some event receivers and creates an item in the relationship lists) we want to be propagated and then executes the SpawnSites timer job.