I recently received tokens from my first ever bounty campaign and I was wondering if it's possible to transfer tokens from my MEW account that doesn't have any ETH yet to an exchange site like Binance?
Transaction costs depend on the exchange to be addressed. Some exchanges like Idex and etherdelta can be directly used with the integration of your Mew account. While large accounts such as binance require you to have a certain amount of gas to transfer tokens and coins.