You can modify the Form through the Form Module, in the "Layout" or "Alternative Forms."
To control what control is used, you can select for each field what form is shown. So if the Message area you don't want it to be dragable, then you may need to use a different form control, or create one for yourself (kentico documentation shows how to do this).
In the form layout editor, you should be able to insert the Submit button using the little tool above it (which allows you to insert the label, control, and validation for each field).
When adding the Online Form, make sure you select the alternative form if that's the one you want to use. Otherwise it defaults to the default layout.