can you tell me where the coins are stored? I mean, where are the coins stored normally in a paper wallet? on a 3rd party?
They are "stored" in the blockchain like every other crypto currency. All any wallet does is give you access to a certain address within the blockchain. This is why keeping the private key safe is important as it gives access to the public address, and thus the coins.
All you need to do is gen an address on the website and sync the wallet. If you really want to test it, send me the public address that it generates and I'll send a coin to it and you can go through the steps I outlined to make sure the process works.
Then why the DEV told us that he do not recommend these services? Why they don't make one official paper wallet generator? Can these walletgenerators website owners store your private keys and hack you later? There's a way to do it offline, you download the website at GITHUB and you can then disconnect the computer from internet and generate a wallet address and private key offline? But my question is, do you need at some point internet, how the blockchain will know I generated that address and privatekey? Sorry for my stupid question.
Then why the DEV told us that he do not recommend these services?
Probably because they didn't make it and thus can't guarantee it has no faults.
Why they don't make one official paper wallet generator?
That will have to be something the dev will have to answer but I'm pretty sure they are busy with the DiguSign development at the moment. Paper wallets are not widely used so I would guess they are low on the priority side of things.
Can these wallet generators website owners store your private keys and hack you later?
That is always a risk yes. However, as you pointed out you can get the code from the Github repo and check it over yourself.
How the blockchain will know I generated that address and privatekey?
The blockchain is just a ledger of every transaction that has happened. It just needs to log that x amount of coins have gone to address y. It doesn't know when an address was made, just when it was first used (i.e coins sent to it). This is how all crypto currencies work. More info can be found here
https://en.wikipedia.org/wiki/Blockchain