Is a wallet simply a folder of private keys?

Is a wallet simply a folder of private keys?

I try to understand how a wallet actually works.

I know there are lots of resources around the internet, but I still can't find simple and concise answers for basic questions about wallets and private keys.

• How does a Ledger Nano S work? Is it simply a wallet?

• Is a wallet simply a folder/directory containing a number (1 or more) of private keys, each able to generate a public address?

  I imagine an entire wallet as a simple text file with a number of lines, each containing a private key (plus some functionality to see the number of coins sent to the public addresses associated with the private keys).

• What ensures that a private key, generated in a wallet, is compatible with, for instance, the Bitcoin blockchain?

  According to my understanding, a private key is simply an encrypted integer value. Shouldn't this encrypted integer value be registered in the Bitcoin blockchain, ensuring it's valid and all other wallets are aware of the existence of this new private key?

• Can I choose my own private key? If I have a favourite sequence of numbers, is it possible to encrypt these numbers and use the encrypted value as my private key, enabling me to have a private key without writing it down anywhere (I know I sound paranoid :-D)

• If I, theoretically, don't intend to spend my Bitcoins, wouldn't it be more efficient to simply write down my private key on a piece of paper and never use a wallet until I actually intend to spend the coins?

• For my hardcore wallet, I am asked to fill out a recovery sheet. How can I recover my funds using my recovery sheet in case I lose my hardware wallet? I'm uncertain how the recovery sheet is linked to the private keys stored in my hardware wallet?

  If I can actually create multiple private keys in the hardware wallet, I can't image how the recovery sheet can be linked to the private keys stored on the wallet.

• How can I see the balance of a wallet? Is it just the number of coins sent to the public address subtracted the number of coins sent from the public address (do you actually say that coins are sent FROM a public address or does public addresses only exist for the purpose of receiving)?

  If that's the case, could I simply dig down my hardware wallet in the ground in my garden, and still keep track of the balance using the public addresses associated with the private keys stored on the hardware wallet?

• Is there any differences between the terms public key and public address? Is the blockchain technology almost similar to PGP encryption software?

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