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I read about having multiple adresses for payments.

Does this mean I have to create a new wallet for every transaction I'm doing?

Wouldn't lead to end up with a hundret wallets after a few years?

You can use just one. Some like to play it safe, though, and keep an "active wallet", where they have a small portion of their money (especially if they have a lot of Bitcoins), and they keep the rest backed-up (and encrypted) and somewhere safe, locally, to protect themselves against hacks.

Is the wallet just a local concept?

The understanding I got after reading those guides online is like this:

the addresses are public keys

the blockchain knows how much money every address owns

the wallet holds the public and privat keys

is this right?

Precisely.

Although a public keys can be re-created from the private key, so the wallet doesn't have to store that.

And the address is actually a hash of the public key, to make it shorter and more readable.

No, you end up with a single wallet with multiple addresses. FWIW, by default, every time you make a transaction you send the change to a new address, too.

so a wallet is just a bunch of addresses?

Wallet is a bunch of private keys. Address is a hash of a public key which in turn can be produced from the private key.

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