Hi Dina,
1. Depending on wordpress theme and whether you have enough useful contents on the HP, I would suggest using a static page for Homepage. If you simply have a blog with different articles, I would use the latest posts as homepage.
2. I use categories as the top navigation header so i wouldn't use no index/follow on that but i would put no index/follow on archive and tag pages to prevent duplication. Furthermore, pages on archive/tag pages should already be under Category so it doesn't provide search engines anything useful/unique so it makes sense to make it no index/follow.
3. If you use static page for homepage, it will have unique contents and provide visitors with useful information so you shouldn't put no follow/index.
4.I say depending on how much of the latest post it is showing. If it only show snippets, i wouldn't put no index/follow since you do want your HP to be found/crawled. However, if it displays the whole post for all of your latest posts, then yes.
5. I like to have breadcrumb so that visitors and even bots can track the path to a certain page. but for user experience purposes, i would include breadcrumb.
6. I would put recent posts/popular posts if it is useful for visitors. If it helps visitors find more related posts that they are interested. go for it.
7. Yup, social sharing helps your posts get more visibility and increase traffic. Recommend using it. Once again, if putting related posts help reader navigating the site / finding useful contents. Go for it.
Rule of thumb, provide good user experience