Can I delete or clear a whole chat?

No. Playbox has no option to delete or clear a whole chat yet, neither a game chat nor a personal chat. You can mute it instead: open the chat and tap the speaker icon (“Mute”) in the chat header to stop its notifications; tap it again to unmute. The chat stays available.

You can delete your own messages one by one: press and hold your message, then tap “Delete message”. You can’t delete other people’s messages. “Edit” in the same menu changes the text of your message.