Identifying another computers MAC address could only be helpful if the Access Point only allows certain MAC addresses to connect to it. You could spoof it and so be allowed to connect.
However, if you can connect to the AP, and you want to do port scans, you should look into
Nmap. There's tons of tutorials online regarding how to perform different kinds of scans, but getting a crude,quick map of the network would just take the following (or similar) command:
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nmap 192.168.2.*
Once you've identified what ports are open on what computers, you can look for possible exploit routes.