Now I'm not sure but both these scenarios can be answered with 1 answer. What you deposit or withdraw is instantly pegged to USD value and not Bitcoins. They might have a third party implementation like shapeshift or changelly where they will insta convert deposits and withdrawals.
Not really mate! The concern is only with the fiat value pegging! Are you saying that once I deposit the bitcoins at 10k EUR exchange rate, the entire time it stays in the game will be valued at the same rate? Same thing will apply while withdrawing as well?? If yes, then have you considered the risk behind that?? People will start using this gambling website for hedging purpose then! It's unrealistic!
The most realistic way is to implement crypto wallet and consider crypto bets in crypto units only so that the exchange rate fluctuation doesn't come into play! That's the simplest and most realistic solution!
That's exactly what gambling sites end up being for most crypto traders. I will not name any sites or any particular person or website with a similar setup but you can easily find many reputed ones if you google around. And this ends up benefiting exchanges more than the players tbh.