I have some apps in mind to control things in my Mac from the iPhone. Probably the simplest thing to do would be to make the iPhone simulate a keyboard and then handle key events on the mac.
What do you think it’s the best way to communicate iphone with the mac? Can I use GameKit for that? HTTP?
You can’t use GameKit, because that framework is not present on the Mac. The way to do this is using NSNetService and NSNetServiceBrowser, which encapsulate using Bonjour to autodiscover available connections. I’d check out the sample code (“Bonjour Web”, “CocoaEcho”, and others) to help you get started.
Be aware, though, that these classes look pleasant enough at first, but can be the source of endless frustration. (They were for me)