"I am wondering if it may be better to have one page dedicated to the specific material properties, one page dedicated to specific applications, and one page dedicated to available types. "

^ this. Create a page targeting each type of customer (one looking for a specific material, one looking for a specific application and one for available types). You can use similar content with some quoted content blocks on each page, just make sure there is unique content there as well that tailors the content searching for a specific need.

I would not noindex the quizzes, especially if they are getting links and shares. If you add a paragraph or two about what the quiz is and how to interpret results (or average results, other info about the quiz), that should be enough content for search engines to determine the page relevance (in combination with the links/shares it's getting).

Another way to add more content is to encourage users to share/comment on their results.

Nope, you are fine.

Duplicate content = 2+ copies of the same text on 2+ separate indexable URLs

Should only have 1 H1 per page... ideally containing the target keyword. If this were a blog post, your H1 would be your article title.

H2 would be used more for subheadings, i.e. if you split your article up into sections with subheadings, each should be an H2

H3-H6 are just sub-sub headings, etc.

Overall, I believe H1 (and perhaps to an even lesser extent H2) has any SEO value - even though it is very minute since it's easily gamed.