Hello, I'll try to answer your questions.
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Only if you think that it can be useful and reusable in other projects.
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Could be a good idea ... but why with an external package ? you can do that without any package.
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Seems to be like a similar approach as 2.
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Seems to be like a similar approach as 1.
Yes Laravel is still a good choice for building a full API application. But I'm not sure what you are trying to do ... if an application is a full API one, that means that you don't have any frontend and only provide services (via the API) to developers.
If your application is a full API one, then yes you need to use a frontend like React, VueJS, ... And you have 2 choices : develop the frontend inside the Laravel project or develop the frontend as a separate application.