Welcome to Medium! I’m not sure if this is the best answer, but I can describe my experience with Medium and hopefully it helps.
I started publishing on Medium because I was having trouble getting my work published elsewhere, I joined the Medium Partners Program to earn some extra cash that could help me continue writing and it also serves as a great motivator.
Medium is moderated by Editors and Curators, who select best stories and hence will promote them in a category or a ‘tag’.
As for reading other Medium writer’s work, you are not being paid to read other writers’ work; unless you’re a paying member (Which costs $5 / Month) which allows a member to gain access to unlimited stories.
Depending on how many stories you like, the $5 you pay per month ends up being distributed to your ‘Liked’ Articles accordingly. (More in Detail on the Medium Partner Membership program).
As for publications and views, Publications often publish your work or promote them on their own websites or other platforms, which is where you’ll see random views being generated from.
Some times articles go viral for no reason, I’ve had some of my pieces reach 1K views and they weren’t even my best work.
As for the platform of Medium itself, it’s established as a form a Social Media engagement — a Cross between Tumblr and Twitter; you’re free to express your opinions on topics you care about and write accordingly.
I personally write about subjects that matter to me and hope that curators or editors take notice.
There are others who (may) employ tactics, such as ClickBait, Self-Promotion, Media Promotion platforms, etc…to gain traction on medium.
As for the grammar, unless you’re publishing with a publication; it’s entirely up to you how you wish to write.
For example, I like to write how I speak and it helps resonate with my understanding of how I’d like my work to be viewed.
Other than that it’s a great platform for me to vent and maintain a Writing Portfolio and hopefully gain exposure to publishing platforms.
Kind Regards and Good luck,