Donna, I'm sure by now you've had all your questions answered. In short, leasing a property varies from Landlord to Landlord, property to property. Generally speaking, you'll have to pay an Application Fee just to have your file assessed by the Landlord or Landlord's representative. The lease term is negotiable, however, the term is usually a year.
Month-to-month leasing is an option once that initial agreed upon term is satisfied. Some rental units do offer the utilities, and some offer no utilities. You, as the tenant, would be responsible for getting those utilities set-up in your name. Appliances also vary from property to property.
All of these questions, while they vary from property to property, can be answered PRIOR to ever stepping foot inside the rental unit. When you are ready to tour rentals, then you should only have 2-3 units you are interested in touring. In addition to this, all your documents to apply for the lease should be completed (with the exception of the lease property details). Preparation is always key to ensuring you position yourself to get approved for the lease you want.
Talk with your REALTOR to make sure all these details are discussed and completed BEFORE you submit your first application. Also disclose any issues that you think may hinder your ability to be a prime rental candidate so your REALTOR can negotiate on your behalf.
If you ever have any additional real estate questions or concerns, please feel free to contact me. I hope this information helps you in your future endeavors.