I edit some post on Wikipedia and inserted my links. Automatically after a mean time, they were removed.
How would I get backlinks from Wikipedia?
You will only get backlink if your link is too relevant to the Article or else Wikipedia team will remove it and ban your account
If the backlink is naturally created by them, how would my blog get benefit in the terms and SEO.
I checked your site and sorry to tell you that its next to impossible to get a backlink by them because of niche. And benefits are that you will get immense amount of targeted traffic and it will be to awesome for SEO of the blog.
It is almost impossible to submit low quality or low DA blogs to the wikipedia.