Because those are the name/value pairs for the form. Every form is going to have something different there. The one in my image is from a XHR request that this site uses to check for new replies to a thread.
Yes.
That example doesn't need break points, it's a simple form where you'd just modify the DOM with the inspector tool like you mentioned above. Find the <input> tag you want to change and modify it's value attribute.
The school's website used a JS library to scan a QR code using a webcam and took then made an XHR request with the data to perform the login. That type of situation is where you need to use break points and it's done via the Debugger tab in the XHR Breakpoints panel. Click the + to add one and enter some URL text to stop on.
You probably saw it in the Cookies panel. Like everything else, there's nothing to stop someone from modifying that value to whatever they want. Like the product ID though, it doesn't matter much if they do. Most likely whatever they change it to would be invalid and just result in them starting a new session. If they did happen to change it to another valid session ID then they'd inherit that session. This is why session IDs need to be long, random and should not shared.