Yes. Always give the hotel a heads up that you will be checking in with your service dog. The same rule applies if you are flying with your service dog. Call the airline when making your reservation and ask their guidance about the best seat, based on the kind of aircraft, for you and your dog.
Ask hotel staff for suggestions about where to take her. Service dogs need to be comfortable going potty on any surface, since there may not always be grass available. To practice, take your puppy out on your street or sidewalk for her first potty of the morning (do this a few times before your trip to make sure she okay with it). Praise and reward for going potty on pavement. And, of course, always bag and properly dispose of puppy poo.
When you make your reservation, tell them you are traveling with a service dog and ask for a room on a low floor near an exit. A dog past 4 months old, if pottied before bedtime, will not need a potty break in the middle of the night unless there is a tummy ache involved.
Depends on the age of the dog. Under six months, maybe every four hours or when the dog indicates she needs a break. Over six months, whenever the humans need a break or the dog indicates the need for one.
After a dog has all of her shots, rest areas are fine. They are usually kept pretty clean. Be careful of areas around fast food restaurants, gas stations, and such. There can be a lot of litter, even broken glass - things you don't want your dog to be around. Parks with hiking trails are a wonderful place to take a break, too.