Your best bet, I think, would be Medium. They are free and published posts will be visible immediately. There is, of course, the question of your niche and which platform to use. A site like Daily Blog Tips will definitely accept posts on blogging and internet marketing, while Web Design Ledger looks for posts on web design and development. Hopefully others will come and look at this thread and give your further suggestions.
You simply cannot post blog posts on high authority blogs. Your article must be unique and of high quality. The foremost step is to build a good relationship with them. Share their blog posts on your social networks. Comments on their blog. This will help you to build strong relationship with them. In this way, you are able to submit guest posts on high authority blogs.
Correct, You need to build a relationship with those bloggers. Connect with them and engage with their contents. Comment on their blog posts regularly. Then they will definately accept your guest posts.
Find the blogs you want to guest post on and email offer to create content for the site owner in return for some hardlinks. also stress the article will be unique and not found on other sites. I generally don't accept these but do agree they are beneficial to both parties.
If there are such blogs then I am sure they can maintain the quality of their blogs for a long time because more low quality articles will come and they will make these blogging sites decrease quality.
The first thing is, guest blogging has a huge impact on your search engine ranking factors. What you have to do is, find out an appropriate and relevant guest posting site to reveal your thoughts with creating backlinks.