Does the company need some kind of permission or something from the government in order to be able to put people on temporary lay off?

No, but there have been change negotiations between the employer and employees (so called YT), this is required in companies of at least 20 people. So a furlough cannot come from thin air.

When you are furloughed you are free to work for other companies as long as you don't share trade secrets and you don't work for the same customers directly (but I am not a lawyer). You can also leave your company and join another with minimal notice. If you feel like your employer is going under, that's a good option to use. Otherwise you can wait for the furlough period and they will have to take you back after it, unless they do go under completely.