Generally, you need to have your own Experience Fragment (EF) template to create the Experience Fragments so you can see all of your styles and exact look & feel of your content. Therefore, EF is kind of editable template on the code side. So, it is recommended to use to with the editable templates. However, you can still use with the static templates and many people implement this with static templates.
No. For experience fragments, only editable templates can be used, static templates are not fully compatible. Editable templates, which in turn are defined by editable template types and an AEM page component implementation, define the allowed AEM components that can be used to compose an Experience Fragment. The experience fragment is an instance of an editable template that represents a logical experience. Experience fragment variations adhere to the editable template, but represent differences in experience (content and design).