Hi,
is it possible to receive several payments on only one adress ?
Yes.
Or is it necessary to create a new adress each time you want to receive a payment ?
No, but it is recommended that you use a different address for each payment. Wallets will automatically give you a new address every time you request an address to receive Bicoins at.
Is the wallet doing this automatically ?
Wallets will track all addresses in your wallet, even if they have already been used. They will also give you a new address whenever you want to receive Bitcoin because it is recommended that you use a new address for each payment that you receive.
Does it create a new adress each time I do a payment ? I mean to stock the leftovers bitcoins ?
Yes. That is called a change address. Every time you spend Bitcoin from an address and there is leftover (i.e. change) that has to be sent in another output of your transaction. Some wallets will send it back to the original address, but most will simply make you a new change address and send the Bitcoin there.