Yes most of that would be illegal, except you gave them consent in your contract or other legal document.

This is also exactly why I always check all the paperwork for "personal usage" of the devices and services provided by the company (email and stuff). If there is nothing about it, I send my mom a random cat picture from my work email (always outside of office hours, in other cases it could be a contract violation). Why? Because if it's not forbidden, you are implicitly allowed to and after at least one private message was sent by the account, it's legally like a private account.

If your employer snoops in the account, it's a massive privacy violation (Datenschutzgesetz and DSGVO/GDPR) and a strong case in employment law. Never needed it, but it's better to be safe than sorry.