Authenticate by Console, API ou C#

How to authenticate hotspot mikrotik console, API or C #? I want to create a page and send external authentication pro Mikrotik which is authenticated

You can’t authenticate users through the API protocol.

The best you can do is have a web page with a form that has an “action” attribute pointing to the hotspot’s login page. That page can in turn redirect back to your site.

I want to authenticate to MySQL or Oracle depending on the configuration that my client choose. I managed to send authentication via jQuery Get Request, but I do not know the answer MK, is authenticated or not. If I use RADIUS would be easier and better?

Yes. You can configure the hotspot to use RADIUS, and it’s probably going to be easier, especially if it’s something like FreeRADIUS (since it uses MySQL).