Those shows you are referring to are from the iTunes store. They are from 3rd party and are the price to own an episode or series. Apple TV Plus is a streaming service for Apple original content.
There are currently 11 series and 2 films, with more added each month. You can see all of the content available by scrolling to Apple TV channels and selecting the Apple TV + icon. The service was launched a mere 3 months ago so of course there is not much content right now, but it is going to grow. All of it would remain free while on the trial. Your ID is tied to your current location so of course it would not entitle you to accessing it in another location, that would apply to all serviced and purchases that are under that account. Those would also be standard terms for other providers.
Other services have licensed content on top of originals produced for the service, however none of them entitle users to a full marketplace and do cost more as well.