Forti AP problem

First I wouldn't put "problem" in the subject line. Use "questions" instead. I thought you were in trouble with a FortiAP.

Access between clients are allowed by default when you create an SSID at the controller, either FortiCloud (they change the name to FortiAPCloud under FortinetOne) or FortiGate. To disable, enable "Block Intra-SSID Traffic".

For the second question, the config would be different between the cloud and FortiGate(FGT). At cloud, it's a radio button selection at "LAN - Allow - Deny", but at FGT, it wouldn't be allowed unless you bridged SSID with LAN or set a policy if you set a tunnel mode SSID.

When you create an SSID there is a setting "Block Intra-SSID Traffic".  It is off by default meaning traffic will flow from one client to another on the same SSID without being protected by the firewall.

The access to your local network or anything interface is controlled by policies so yes you can block your local network.