Is it possible to send from and receive back to exchange adresses on Bitstamp/Bitfinex, or do I need to have a dedicated wallet to process the bets?
You can send directly from the exchange, but if they do not process withdrawals automatically and immediately then it may not be suitable for time sensitive bets.
As for receiving the winnings back to your exchange account, I'm not sure how Bitstamp/Bitfinex operate so it's best that you ask them.
We will send your winnings to any Bitcoin address that you provide.
If there is a deposit address in the exchange that is dedicated to your account and to your account only then it should be fine.