Post fields and post submission

...but what about the file inputs, how do they understand post status?

They inherit the post status as specified in either the title or body field. Bare in mind, that by default, one single submission from the form creates only one post so post fields on the same form share some settings.

What happens after the post is submitted? How do i print all the post fields input values on a theme page (including images) ?

After submission, the form entry is used to create a post. Gravity Forms does not handle how the post is displayed in the theme; however, using the "Create content template" option of the body field, you can configure values submitted on the form to be displayed in the post body.

I see in total three different options of uploading images: 'file upload' in advanced fields, 'image' in post field and a 'custom field' where i can choose 'file upload' from the select box. What is the difference between this options?

The File Upload field lets you upload any file type. The Post Image field allows you upload only images and is automatically added to the created post's gallery. The File Upload option of the Custom Field field allows you to upload any file type and populates the specified custom field with the file's uploaded URL.