Is there any free Weather API?

yr.no provides a lot of global data for free, but the API is a bit funny to use (though a new one is to be released sometime soon).

The US NWS provides a huge amount for free, but the data is US-only and it's quite weird to use as well. https://www.weather.gov/documentation/services-web-api is something to start with. A lot can be found on FTP sites as well, like radar data.

It depends. OpenWeatherMap has a free plan: https://openweathermap.org

I use OpenWeatherMap. Which has a pretty great free tier. Many APIs are "free" at least to some level, though if you are hoping to pack the API key in an app you ship to millions of people, expect to pay for it. APIs cost money and server resources to run, the free lunch is only ever going to extend to a certain amount of use.