Not yet. Currently, the preferred media player by the gPodder project is the build-in media player, as we now have great resume and position tracking support since version 2.8.

There's a "Delete episodes" button in the gPodder main window and in the "All episodes" window. You can also delete episodes one-by-one by long-pressing on them and choosing "Delete" in gPodder.

Use Media Player and select the episode from gPodder's "All episodes" view.

Not yet. That depends on the availability of a time stretching module in GStreamer, and support for it in either Panucci (more likely) or Media Player (less likely, because MAFW is complicated).

Actually, the black window that appears right after you click on the icon is just a fake window from the window manager to make the startup feel faster. What you see is that gPodder takes too long to show its initial window, which makes the window manager hide the fake window again (you can test this by clicking on the task switcher button quickly when the first window appears - you'll see that the window isn't visible in the list of open tasks, because it is not there yet).

There's nothing an app developer can do except make application startup faster, so that the fake window is still visible when the main window is first shown. My time is limited, so right now, I'm spending more time on improving the user experience and fixing bugs and after that, I might have a look at optimizing startup time (but anyone is welcome to jump in and submit patches - gPodder is an open source project!).