I have some experience using/writing HTML. FR accepts/uses just the HTML basics. If you include CSS or Javascript in your submitted HTML, you’re going to be disappointed.
For an example of nested tables that FR will accept and render well, check out the posts at the FReeper Canteen:
https://freerepublic.com/focus/f-news/3667932/posts
https://freerepublic.com/focus/f-news/3667631/posts
https://freerepublic.com/focus/f-news/3667392/posts
Have you tried using your brower’s ‘view source’ command? I use Slimjet and can type Ctrl/u on any FR page to see the source code rendering. This can be very helpful in debuging your HTML code.
Here's the table on my website.
http://www.iment.com/maida/politics/trump/for-ransomnote.htm
Here's the table on FR.
http://www.freerepublic.com/~mairdie/