As a workaround to the first question, there is a 'remove first image' option under structure detection you can use during conversion to delete the embedded cover, which is typically the first image.
The margin issue is that mobi on Kindle only supports margin increments of 2em, so a slight margin in the original file could get rounded up to 2em. There is an 'ignore margins' option under Mobi output to help resolve this, though you will lose all indented paragraphs as well if they're purely using css. The solution for retaining indented paragraphs is to use <blockquote> tags, as that's the native mobi method for defining an indented paragraph. Nest blockquotes for multi-level indents.