How to get an actual execution plan from the linked server?
I don't believe it's possible to get the execution plan via OPENQUERY() remotely, and the only way would be to connect to the server directly and run the query there, unfortunately.
That being said, you should definitely see an instant performance improvement for all of your linked server queries, if you migrated the remote server data to the local server (e.g. via one of the data synchronization features such as Replication or AlwaysOn Availability Groups), assuming your local server can handle the additional query load. Just an idea.