Calling webapi outside appian

Web APIs are supposed to be created to allow a third-party system to get data from Appian or cause Appian to do something, so obviously Yes they can be called outside Appian. There are plenty of option for consuming a Web API, you can google that out pretty easy. The most widely used platform is Postman in which you can do almost everything including design, build and test.

To call a Web API FROM Appian, you would is a connected system and an integration object. To provide a Web API that other system call TO Appian you create a Web API object.

...and don't forget that it doesn't matter whether the a Web API is called from Appian or another external system, you still need to authenticate when calling it. There are choices about how you authenticate but you can't successfully makes calls without doing so.

unless that API is open like this one. 
api.spacexdata.com/.../launches

I was able to call the Web API through postman using basic authentication which requires an admin user ID and password but the problem is that the password will expire after some days so at that time the authentication will fail, so is there any other solution to authenticate? And are there any options other than basic authentication to call the webApi

You can use API key authentication, it is more efficient and secured also. Check API Key authentication

I highly recommend to work with the official Appian documentation. Like this: docs.appian.com/.../Web_API_Authentication.html

Could you please elaborate on how to generate the key and the value if we select the API key as the authentication

Please read the documentation first. If you have any specific issue, we are happy to help.

This is very basic question, if you read the documentation it will answer such questions.