Technically possible with a layer 3 switch but routing is still required and best done with a purpose built router.

If he’s terminating each end too and has the equipment get him to test and certify each cable for you. Means you know they were working before he left. Proper labeling of each end is also essential.

Never run a single cable when it’s just as easy to run 2 or more at the same time. Gives redundancy and/or expansion.

Do an ipconfig /all and get the Mac addresses of the adapters. Then do a Mac vendor lookup on them to see what they are. You seem to have a pretty big local subnet.

Yes, this is called WDS. Not usually the fastest or most reliable but it is possible.