Not sure on how many tokens you can have attached to one address, I can't see why there would be a limit.  In terms of security MEW is not a wallet, it is simply an interface which allows you to view and manage your wallet, security is down to you as you hold your private keys. 

If you always log into MEW by entering your private keys each time then you are exposing your keys each time you do this and if there is a problem with MEW this is where you could come across problems.

Try if you can to use a hardware wallet to log into these sites as it is much safer.