1. PDF forms can be filled offline, saved locally, and form data sent when you are next online.
Do HTML Forms possess the same functionality?
--> So yes and no. Out of the box, HTML forms are rendered like any other HTML form and therefore have no offline experience provided at all. However, if you use Workspace as part of interaction with a long-lived process then yes. Users can fill in, save, entirely offline and sync is taken care of entirely for you.
2. HTML5 browser-based forms can be viewed on both mobile devices and desktop browsers.
Could PDF forms also be viewed on both mobile devices and desktop browsers?
--> No, interactive PDF forms have no support what so ever for mobile device. Use PDF as DOR (document of record) and HTML as your primary data entry mechanism.
3. I see that Adaptive forms is the third type of forms.
Does it mean that PDF and HTML5 forms are not adaptive?
--> Exactly, HTML generated from XDP are not adaptive. They are fixed position-based.
4. When we select "Create Adaptive Form" in AEM, are we creating PDF or HTML5 or neither of them?
How to create PDF or HTML5 Forms? What is the interface?
--> Neither, Adaptive Forms are not created in Designer. It is a dedicated interface built into AEM Forms. Entirely web-based. The documentation is fairly high level but it will give you an idea of the features and author experience: https://helpx.adobe.com/aem-forms/6-2/topics/author-adaptive-forms.html
