This will vary wildly depending on many different factors. In general, a movie will come to Prime Video after it loses popularity at the box office, and that typically takes anywhere from 1 to 12 months. That said, competition can snag exclusive rights that keep a movie from coming to Prime Video indefinitely.
This depends on many factors that include the popularity of the content, the studio that produced it, and the many legally binding agreements that dictate publication rights. For most content, you can expect it on a streaming service within a year of its original release, but that doesn’t guarantee it will be on Prime.
There is no simple or short answer to this question. Amazon’s ability to air a show on Prime Video depends entirely on contracts with the copyright owner, and those contracts come in all shapes and sizes. A show can be available anywhere from the same day to years later, or even never if another site gets exclusivity.