A two months notice resignation letter suits senior roles and contracts with a long notice clause. Because the runway is long, use the letter to propose a concrete handover plan — that is what turns a long notice period into a good reference.
Whatever your employment contract specifies — commonly two weeks to three months. If the contract is silent, statutory minimums in your country apply. Check the contract before you name a last working day in the letter.
You are not required to. 'Personal reasons' or 'a new opportunity' is enough. Detailed complaints belong in an exit interview, not in a permanent file document.
Usually yes, and it creates a timestamp, but attach the signed letter as a PDF. Many HR systems require the formal letter for the personnel file regardless of how it was sent.
No. Resignation is your decision. An employer can hold you to your contractual notice period, but they cannot refuse to accept that you are leaving.