It’s hard to estimate an average monthly rent in the capital because prices vary from area to area and it all depends on your preferences and budget. But here’s a rough guide on general pricing to get you started:
Yes, you can. The majority of people who move to Serbia don’t have a temporary VISA when they first arrive because you need to apply once you’re living here. Estate agents are used to dealing with this situation and will make sure your contract includes all the information required when you apply for your VISA.
No, you don’t need to open new accounts. In Serbia your contract either includes the expenses in your monthly rent, or the landlord will send you the bills per month and you pay that on top of your rent. You don’t need to transfer anything into your name apart from the contract. This is much easier for both parties.