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I would suggest you use CAT 6a cable to connect the two. Use Cisco 1000BASE-T Copper SFP on C3560.You may save a 10G port for something works at that speed.
You may use RW community to direct switches to upload its configuration to a TFTP server, then check for that on TFTP server.Or you may enable HTTP access to run something like `show run | section aaa`.