Is a trial subscription to Apple TV only good for viewing two episodes?

On Fire TV devices, you can’t currently buy, rent, or subscribe. The financial step has to be done on a different supported device (e.g. iPhone or web). Once that is done, then you can watch on Fire TV.

2. On Amazon Fire TV, Android TV, and Sony TV devices, you can't purchase content from the Apple TV app. You can buy, rent, or subscribe on another supported device and then watch in the Apple TV app on your Amazon Fire TV, Android TV, or Sony TV device. [2]

There is no one month trial for Apple TV+, as far as I know. There is a 7-day free trial for regular new subscribers. Or an extended free trial if you recently made a purchase of a product or service that qualifies for that extended trial offer.

A trial subscription to Apple TV+ should give you the full experience of a paying subscription, with access to all of the Apple TV+ content. A select few episodes for certain shows may even be available before subscribing. It sound like you are not signed in, or your subscription isn’t recognized.

On what device are you trying to watch Apple TV+?

Did you sign in to the app with the Apple ID account that has the subscription?