Pentesting on WiFi

Hello people ...

I have a question related to pentesting on someone's WiFi network.

That WiFi network is located in pizzeria near my house. Is it legal to scan that network, do recon, find vulnerabilities and try security of devices? There is main computer that is using Windows 8/10 and is being used to sync orders with pizzeria's website and to things related to that. So if I will try to put backdoor to that PC and it will success, and then I'll report vulnerabilities to that pizzeria's boss (manager), am I breaking the law? I mean if I'll do pentesting without permission before that.