How to authorize the router through the Web authorization of the WiFi access point?

Question

WiFi

1. We have Wifi, but when you connect to it, an authorization window appears, after entering your login and password, authorization passes and access to the Internet opens. And what about the router? Do I have the ability to connect to a wireless network in my router and receive Internet from it? There you can select a network and enter a password for it. And how to enter the login that is required on the authorization web page, and there may be additional fields. How to pass this authorization in the router?
2. Strange, but for some reason, in the router, access to the Internet is still opened without entering a login and password at all. Just connect to the network and the Internet is. Is this a bug with the developers of the authorization system? Or does he somehow remember the authorization that was previously carried out on the computer, through a direct connection to the network?