Whether do/no follow link, Wikipedia links are great for driving traffic to any websites, given that you can get and keep that back-link. For SEO purposes, it is always a great idea to diversified links to appear some-what natural (but we all know that link building isn't natural).
Yes, they will help. wikipedia is the best trusted sources for Google and having a link in that means having a dinner with Obama!!
Yes. Wikipedia is always treated as genuine source to collecting information. If your website is placed inside wiki then the backlink is very powerful just like edu and gov backlinks. The wiki site mostly operated by private parties and they generally delete spamming content. This is the only drawback of this wiki posting works
IMO, Wikipedia links are the most powerful links to boost your SERP in google. But, It is not possible to get links from Wikipedia.