I'm still a newbie to cryptocurrency industry. I recently joined in a few airdrop events. But, still I have 0 tokens available in my MEW wallet. Should I have some Ether on my MEW wallet in order to receive tokens?
No, you do not need to keep the etherium for getting tokens. You need the etherium only for sending tokens from the MEW. Perhaps you don't see the tokens, because they are not yet added to the MEV (after ICO, for example). Use the site
https://etherscan.io/ to monitor the receipt of the wallet. You don't need login into the wallet every time.