Your ideas on how to handle that outlined above are fully correct. There is nothing bad about having a lot of files in the project. It does help a lot when you want to reuse code or if for example login details change and you don't want to edit multiple code locations.
Nevertheless, you may combine in such simple cases model class and controller class, especially if your model data can for example be stored in an NSDictionary
and such. Only if you have complex model objects, that will run a lot of their own code, it will be better to separate them out.
Variable and method names can't be too long ;) always use a good name that especially describes the functionality or task. You usually don't have to type them often, but Xcode autocomplete will deal with that easily.