Establishing a Successful Trace in Public Wifi: Does Login Page Is Enough?

Dear null-byters, it's me, a lifetime learner, Jacob. I'm here again wondering if you could answer my questions (I'll ask based on my current knowledge so,I'm sorry if it sounds stupid or too easy to answer).

Let say, we use a non-personnel WiFi, but the problem is, we need to log in first (like at the workplace WiFi which requires a login information (a registered username to be specific ), and we started to hack a website, but if we got tracked, does this means that we could easily being caught due to the log given to our ISP? And how do we leave without any trace? And is there any way to get an internet connecting by bypassing the login page? Or, finding a full list or user and their password could be helpful.

Regards,

Jacob.