This is a very opinionated answer, be aware that some would not necessarily agree with my interpretations and beliefs.
Improving your writing widely varies whether it is just for general improvement, or writing for a specific purpose like academic papers.
From my non-native speaker perspective, I would rank this as the easiest form of writing. Sure it does sometimes requires big fancy words unbeknownst to mere mortals, but much is forgiven there as the content prevails over the form. From your post I would say you are ok there, you are an efficient communicator, there are some grammar and style issues but they aren’t too hard to fix. My recommendation is similar to the other answers, review your grammar, read, write.
General informal writing
Here the goal is to sound natural, and notice that I did use the word “sound”. Some academics are not able, or unwilling, to loosen up and ditch formalism and the big stick logged up there. Most of the sentence structures and words used in a scholarly context are contrived and unattractive, they may be precise, efficient even, but they are platypuses that don’t quack right.
While your question post was clear the sentences seemed a bit like bullet points in a presentation, a bit too dry and robotic for my taste. You could try to add more structural variations and different sentence lengths. I know you asked for a “formula” to improve your writing but I would argue that what you need is less, and not more, rules....writing is a soft skill.
To improve in this area I would pay more attention to spoken English. This in turn would help you write dialogue, if you ever need to.
While estimates vary, there are only three to five thousand words commonly used in the english language, you don’t really need more. Some of the world greatest authors use very simple vocabulary that can be understood by a child.
Also, for general improvement practice is key. As in other fields the 10 thousand hours of practice rule of thumbs apply.
The First Million Words Are Practice
Fiction writing is too vast a subject to address quickly and is the reason behind forums like this. This is writing as an art form. Many how to books are written about it, Here is one of the most prolific authorstake on it:
20 tips from Stephen King’s On Writing
In your case I think you should start by writing poetry. Poetry follows many rules which should keep you happy, yet, if done properly, flows. Writing is music, pay attention to the rythmes of your words, you should try to read aloud what you write, it should improve your flow. Also it can be healthy to ditch the rules and be nonsensical. Try your hand at free form writing. A lot of writers enjoy playing around with words. Again this subject is too vast to do it justice in a post. I will leave you with the example of a mathematician who knew how to loosen up and be “silly”. (not to mention a certain scholar who doodled aimlessly that in a hole in the ground, there lived a hobbit)
Alice in Wonderland’s genesis