Can I place list tag elements between "h1" heading tags, or are there some kind of rules saying this is invalid?
I have never seen anyone put "ol" and "li" between <h1></h1> tags, but I am not sure the reason. Is it because it is bad for SEO?
h1 is a block element and will only accept inline children (span, img, etc).
ol is a block element, and it would be simply wrong to put it inside a heading element as it is not semantically viable, since it is probably incorrect to assume that a list can be a title of a page.
All this would make your SEO not working.
A bit more info here: http://www.w3schools.com/html/html_headings.asp and there stackoverflow.com/questions/4041820/are-h1-h2-h3-h4-tags-block-or-inline-elements#answer-4041841