Some information that may help you understand things a little more. You should probably think in the context of threads though, not actors, for the purpose of your question.
The default backend is Akka HTTP (previous versions - prior to 2.6 I think - shipped with Netty by default, which is still available in later versions as a configurable alternative backend to Akka HTTP).
Play's default execution context is configured to pool 1 thread per processor core. The docs state processor but more specifically it is per core. The assumption is that you are building your application in a purely asynchronous and non-blocking fashion though - core tenets of Play's architecture. If you need to do blocking work (notably synchronous IO) then you explore the concept of having a custom pool where you control the number of threads available, and/or multiple pools which provides you with a way to isolate your blocking work from your non-blocking etc - please refer to the docs.
If your thread pool(s) is/are exhausted then subsequent requests will stack up. Default timeout configuration settings can be found by consulting the play docs, or more specifically, the Akka HTTP config.