In Switzerland the notice periods depend first on your contract and if not mentioned on the Swiss labour law. Normally the notice periods are three months and at senior level even six months. The length of the periods are the same for both parties. Normally you have to give written notice and the notice period starts at the end of the month. However, you may agree on different terms.
A dismissal basically doesn't need a reason.
In Switzerland you are assured for unemployment by the state. Please check the official website: