What will happen with my coins stored on my wallet? Are they save after this operation and hard fork? Or do I have to send them to Cryptsy for example first and take them back afterwards?
Your coins in your wallet are safe, it's just a client update, just have to download the new client and you're good to go!
Ok, so I have to download and install a new wallet when the client is updated. Do I have to replace any .dat file or backup something?
Is it so that when I only start the new updated wallet, everything is ok?
Ok, congrats
You do not have to touch anything except for what comes with the new wallet.