Are both servers on same domain or different?

error screenshot could help in digging into the issue.

There is no need of Linked Server to configure Mirroring between two databases on different instances.

You just need to check these points:

There is connectivity between both the instances.

Both the instances...

If you want to free the space at windows level, then Shrinking is the only way, no other alternative.

and yes, as other said, do rebuild the indexes.

Also, set the auto_growth...