When I am at the public library and try to use their WIFI it says it is an unsecured network.

You can still use it but if you want privacy then you should not use it unprotected. Use a VPN to protect your computer from undesired snooping while connected to an unsecured network such as any public Wi-Fi.

Yes you can, however they are just warning you that it is an unsecured network and not to share any sensitive information on it.