Bitcoin wallets never contain money. The only important content is one secret number. This secret number is called a private-key. In most current wallets, the secret number is instead a seed from which a series of private keys are generated in a predictable (deterministic) way.
The only place you can find out how much money you control is in the public replicated journal of transactions called the blockchain. Every wallet has a copy or access to a nearby copy. Blockchain explorers let you search their copy.
You see how much money you have by making a list of the addresses* your wallet created and looking through the whole transaction journal for mentions of those addresses receiving or spending money and add up the amounts. Subtract the debits from the credits to calculate a balance.
The Bitcoin network doesn't encrypt any data.
You use a new receiving address for every transaction so that senders can't see what other money has passed through your address. For privacy.
You use offline wallets for security - a wallet on a computer that is connected to a network can potentially be hacked into. especially if it is a computer you also use for browsing web-pages and for downloading and playing games. An offline wallet in a computer that is never connected to a network is much safer.
All well-formed addresses are valid. They are just large numbers, all large numbers are valid (you may have to add a few checksum digits) but almost all of these large numbers will never be used because there are so many of them.
You don't have to publish addresses explicitly or separately, you just use them in transactions. Unlike street addresses, Bitcoin addresses do not identify people or locations - they are just a random-looking number without any special meaning. You don't have to claim ownership of an address. You can use mathematics to prove you know a secret number (private key) from which that address was derived. The proof doesn't disclose the secret number. The proof is what allows you to spend money, it doesn't matter who you are. The Bitcoin network doesn't keep accounts for people.
A Hierarchical Deterministic (HD) wallet creates new private and public key pairs as needed (usually a few in advance of need) from one master private key.
Your wallet will take care of all these details for you.
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