Do snapshots retain the IP address of the Droplet they were created from?

No, snapshots don’t retain the IP address of the Droplet they were created from.

We assign Droplet IP addresses automatically and they cannot be manually reassigned after creation, but you can assign a reserved IP address to a Droplet and then reassign the reserved IP address to other Droplet’s as needed. This allows you to maintain the same IP address in your infrastructure but gives you the flexibility to point it at different or redeployed Droplets.

No, you cannot downsize a Droplet using a snapshot.
Snapshot images are compressed when stored.