For your first question: MDR requires manufacturers to establish a QMS (Quality Management System), as stated in Article 10 MDR. For class IIa devices and above, this QMS will be assessed as part of the conformity assessment. For class I devices, an external assessment or certification is not required. In general, ISO 13485 certification is not mandatory, but your QMS will be evaluated as part of the conformity assessment regardless of ISO certification. Many companies choose to get ISO 13485 certification first as a kind of 'final rehearsal'—if you fail, it has no regulatory consequences and can help you prepare for the real conformity assessment.
For your second question: If you are based in Switzerland and want to place a CE-marked device on the EU market, you must appoint an EU Authorized Representative immediately; there is no transition period. The EU AR helps register your device in the local Competent Authority’s database. While Switzerland recognizes CE marking, you still need to register your device with Swissmedic and meet local requirements for vigilance reporting. The Swiss MepV is nearly identical to MDR, but local obligations still apply.
One extra note: Be sure to observe the required languages in Switzerland.