Is it ok to use mutable states with akka PersistentActor or shall I use context.become/unbecome with receiveCommand() and not with the receiveRecover() as it will wait for the full recovery before the state is changed.
In general you can't use context.become and friends within a PersistentActor because those affect the receive method, which is provided by the PersistentActor (and handles some internal messages which are implementation details, so you don't really want to duplicate it).
Being more explicit about the mutable state than context.become is a better path.
There is a pattern of wrapping up all the mutable state into a single immutable object (e.g. a Scala case class) and deferring the command handling to that object, which could be as simple as something like:
var state: State = ???
override val receiveCommand: Receive = state.processCommand(_)
You can go further and have your processCommand method on State return, e.g. a (Seq[Event], () => Try[Unit])... this is actually fairly close to what projects like Lagom or Typed Persistence are doing.