How Bitcoin nodes validate a new wallet
They don't
Bitcoin nodes validate blocks and they validate the transactions within those blocks
Other nodes don't have access to your wallet and can't validate it or anything in it.
I mean, what if this wallet already exist?
No one knows or cares if the private-key initially generated by your wallet already exists. Nodes don't check for this type of "collision".
If someone else's wallet has the same private key, either of you could spend each-other's money as well as your own.
if I create an address offline, how Bitcoin nodes would accept my address as valid (or this isn't needed?)
Any address is accepted so long as it looks like an address. A well-formed address has an acceptable length, initial bytes and checksum.
I mean, in which moment, Bitcoin nodes accept my offline-created address.
each node accepts it at different moments. In whatever moment they happen to come across the address and see that it is a well-formed address.
how this address appear in this web?
A correctly generated well-formed address that has never been used and consequently never appeared in the blockchain is nevertheless a valid address. I expect most blockchain explorers would simply display it and show that there are no transactions associated with it.
In summary, no one keeps track of wallets, private-keys and addresses that have been created and never used. All of these are just as valid as a wallet, private-key or address that gets used a thousand times a day every day of the year.
There's a vast ocean of numbers, they are all valid. Some have been used, some not yet, almost all will never be used.
See also
