student moving to Rotterdam-help needed :)

Hey! I will be moving to Rotterdam in a couple of weeks and I'm looking for a bit of information about getting started. I am an EU citizen, and I will be studying at Erasmus University for a year. I have no employment history in the Netherlands (although I'm planning to get a part-time job), but if necessary, I can provide a Dutch guarantor.
So my questions would be that under these circumstances,
1. is it possible to sign up for a prepaid smartphone plan, or is it only top-up cards for people without regular income?
2. is it possible to rent an apartment or studio (not room!) on the market, or do companies require regular income for that?
3. how many days do banks require to open a bank account?

thank you so much for your help!! <3