Hi realgoonkilla, and welcome!
1) Do I manage my bitcoins on a website or must I download a program? What's the best anonymous website/program?
It's your choice. The simplest way is use an online wallet such as blockchain.info or Block.io. Be careful about any online wallets or exchanges where you send coins! Many people have lost coins due to theft or incompetence of the services they trusted with their coins. The longest established online wallet is Blockchain.info. To really control your own coins (which is what Bitcoin is about) you should run your own software. Again you have a choice. A popular recommendation is using a "lightweight" wallet like Electrum. See this page for a good wallet guide:
https://bitcoin.org/en/choose-your-wallet 2) What's the most anonymous way of buying and selling bitcoins?
I read something about buying and selling directly with people instead of a company?
Yes, it's most anonymous to use a peer-to-peer service like LocalBitcoins.com. For example, to buy coins find a Cash Deposit trade on LBC, follow the Seller's instructions to deposit cash into their bank account nationwide and receive your coins from escrow when done. You never need to provide any id or anything else to sign up for your LBC account. You can sell coins in a similar way by meeting people via LBC.
3) Is it true that you can "delete" your bitcoin transaction history by mixing your bitcoins with other people's bitcoins and then you receive back "anonymous" bitcoins ? If yes, what's the best website/program?
Not exactly. You can never delete any Bitcoin transaction history which is recorded on the blockchain. It's also possible, for example, to use a small or improperly set up mixer where you get back the same coins you started with. It's possible to use Bitcoin anonymously, but proper care must be taken. If you're not confident you know what you're doing, you should assume anonymity is compromised. In general, though, by using many different steps together breaking transaction links becomes easier. For example, send to a mixer, then to a gambling site, then to a throwaway online wallet, then to another gambling or exchange site, then back to your spending wallet. That should pretty effectively give you very different coins than you started with.
JoinMarket is a recommended mixer.
4) When I sell a bitcoin, what currency will I receive and does it go to my bitcoin account or where?
If I handed you a gold ring worth $500 and asked you the same question what would you say? The answer is the same for Bitcoin since Bitcoin is just something of value. The money you receive depends on where and how you sell it. There is no limit to this.
5) Finally, what's the most anonymous/best way to withdraw my money?
You mean sell Bitcoin for a national currency? Probably use LocalBitcoins. There are many different trade options. For example, you might meet someone in person to trade cash, or you might get an Amazon.com or similar gift card code online if that works for you.
Do i have to convert the money?Do i send the money to my paypal and then to bank account?
If you're asking what's the most convenient way to buy or sell Bitcoin the answer is probably Coinbase.com. When you set up an account there you can buy and sell Bitcoin directly with your bank account. However, doing things this way is not anonymous. If you want to be more anonymous, it usually means more learning and work involved.
