Do I roll my two skill dice first and the two environment dice at the same time, look at the result and THEN decide whether I want to reroll one or more of the dice for stamina - or do I roll my dice first, THEN decide whether I want to reroll and when the result is clear, I roll the environment dice - and can then decide again whether I want to reroll any of them.
You roll ALL the dice at once.
After you see the results of all the dice, you then decide your re-rolls.
Can I re-roll environment dice at all - or can I only pay with stamina for my skill rolls?
You can re-roll any die in the exchange. It doesn't matter whether it was your dice or the dice of the environment.
Can I reroll a repeated die due to stamina use?
I think you are asking if you can continue to re-roll dice by spending more stamina.
If so, then yes, you can continue re-rolling dice if you keep spending more stamina.
Those are the rules as I intended them. However, if you enjoy playing with different rules, go ahead! You could decide that you can only re-roll dice from your hero and not the dice from the environment or that you can only perform one re-roll. That would make the game harder of course, but if that feels more natural to you, that's fine. You could balance the difficulty by giving yourself some extra stamina or resolve.
Anyway, thanks for playing "Dungeon Hero" and I'm glad to hear you enjoy it!