Ok I created a wallet on myetherwallet.com and have my private key... I was wondering if I somehow lose access to the myetherwallet.com website or its unreachable can I use my private key generated by this website to transfer my coins (ETH) to for example the Blockchain.info website?
Im not sure if thats how private keys work, I tried searching but couldn't find an answer.
If you have the unencrypted private key then you'll basically have access to your coins forever. You'll be able to access your ethereum in your wallet no matter what happens to your wallet file or even myetherwallet, whether you accidentally clean your cookies or not.
You'll be able to use that private key to access your funds, even if myetherwallet is down, essentially. And once you get access to your wallet, you can then send your ETH to blockchain.info, sign other transactions/messages, etc.
You just need to find a wallet that is capable of doing it, like the official eth client or something. Make sure you back up your private keys securely though, you don't want it to be stolen.