If not how to safelly store Tokens if there is no dedicated wallet?
Yes, you can deposit ERC20 complaint tokens on your MEW wallet. Actually, MEW was design to really function just like that. You can just to setup the ERC20 like decimals places token names etc. You can get it to Dragon chain or to the bounty manager.
As far as safety goes, its still up to us to really protect our wallets. Used strong password and importantly, never type MEW because once you made a mistakes, you will be redirected to a phishing site and chances are you are going to lose all your tokens because they can easily stole all your information including your Private Keys. So I advise you to bookmark the URL.
yes I agree with you, we have to use the key strong and most important be careful for the storage of private key, because it is very privacy, if we misstep, then our money will run out in stealing people, so be careful.