Lets say I create a paper wallet using bitaddress.org which I saw a YouTube video explaining that is best to do this offline, using a pc not connected to the internet before.
I create a single paper wallet with a BIP38 Encrypt (my secret password).
Once I copy-paste into
https://blockchain.info search bar the Share address of the wallet, it can give me all its information e.g. transaction history, final balance, etc.
My 1st question is: How come when I was offline I create a new wallet, and immediately this wallet was available to view?
Every address already exists in the network. When you create a new wallet, you are choosing a random private key which controls your new address. Because of that, you will be able to spend all the coins received and owned by that address. Something like that.
In my understanding this wallet pre-existed.
That's true.
if it pre-existed, how come was it given to me?
Since I did this offline, couldn't another person create the same wallet at the same time at an offline environment and set a different BIP38 Encrypt?
Your wallet just designated that random address to you. Therefore, there is always a chance that someone generate an address you already controls, but this simple won't happen because there are near 2^160 addresses (~1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976) in the Bitcoin ecosystem, which means that it's near to impossible to generate the same address two times in a row.
I can't really comment on your question about the BIP38 encryption because I don't really know about the subject.