It's easy to do that on a single server. I believe it is theoretically possible to do that across two different servers, especially if you are using a query store. However, I believe it would be next to impossible in practice. That's because even if we have objects all with the same name, they may not have the same object IDs. So, there could easily be differences in the plans at a binary level.
Regarding your second question—assuming you have SQL Server 2014 or later—you may want to read more about the basics of Query Store. Details can be found here.