I can't log into my Apple ID account on websites / can't download apps / edit Apple ID settings
Best thing to do in this case is find a working web browser and try signing into iCloud.com or appleid.apple.com to be sure your account isn't locked or you have a password issue.

When that's sorted, go back to the device and try one thing before you move on to the next. Check date/time on the device since most Apple log in are very strictly SSL / HTTPS checked and time being off will block the log in attempt as does network shenanigans like man in the middle type privacy attacks (or "snooping by someone" using http proxy).