But the number is not enough to buy anything or open a bank account. For that you need the physical id card that is as hard as forge as passports.
A very good system to make contracts, paying taxes, school registration, etc easy without allowing false impersonation.
Everybody knows their personnummer by heart, while in Italy most people carry their health card around with the 16-character codice fiscale.
Cannot say about Sweden, but most people I know in Italy also know by heart their Codice Fiscale (whether they carry with them nonetheless the card is another thing).
You don't. For that, you can get a digital signature. You can go to a police station, or to an embassy and present your physical Id card to get a digital signature. You can use that signature to sign contracts or your tax returns.
> how do you apply for a credit card or similar online?
In Spain, with your usual bank, you use your login/password and your 2FA.
In Sweden, you can use Bank-Id almost everywhere to identify yourself. It is also a digital signature, but it has brother use.