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Now do I use this plugin?

When you go to your post editor you will see drop down menu "TOC Levels". Select you chapter and then chose one of the levels. Or you can manualy wrap your chapter in [tinytoc level="lv"]cont[/tinytoc] tags where lv is your level (number) and cont is you chapter.

How to use image as "Back to top" button?

You have to add <img /> tag to your text with path to that image as src attribute value.

Can I add text before TOC?

If you add [tinytoc] after that text, yes.

Can I chose TOC position?

Yes, by placing [tinytoc] in your text.

How can I remove `Header` and still be able to use `Back to top` feature?

In order to use Backt to top you need to have some tag with some ID. Just add style="display: none;" to your Html before title field in tag. If you have default example <h3 id="tyinTOC"> then you would have <h3 id="tyinTOC" style="display: none;">. That will remove Title before table of contents and still allow you to use Back to top feature.

How do I know what each of these fields mean?

Visit documentation.