Your issues is not related to EA, you need to refer to your company "employee handbook".
BUT, in certain specialization especially telecommunication jobs, the company will restrict the employee from talking in their work field because it will disrupting the other who is on call.
(3), For this issues, some people are very sensitive toward word. So the word "stupid" maybe will offence some people. Try to not use it if possible
(4) The company have the right to issues a warning letter as long they feel needed. BUT, you can go to your HR department and ask for further detail (in peacefully). The warning letter only influence your KPI and termination. Termination only if your conduct serious offence or already get certain amount of warning letter (the amount is depend on your company).