I would like to download a game on my laptop (eg from Steam or Origin) and would like to know if my computer breaks down and then I'm on a new sign up, the games I bought are still on the account or whether I have to buy it again.
The games are tied to the account, not the computer. It does not matter if you have a new PC or something similar, as long as you log in with the data you can install your games everywhere.
You would go bankrupt if you had to buy the games again and again.
Games, no matter on which gaming platform, are bound to the account and the e-mail. Not to the PC or laptop!
As long as you have your access data you can play your games, even if you have a new device!
Remember your password to your gaming account. Store it on a password manager on a USB stick, in the cloud… Or quite crazy: write it on paper. Could you then download in Peru in the Internet cafe.
House and computer can burn down as long as you have the passwords. Everything is yours and remains yours.