I have written this paper and I would like to ask, via email, from some professors in other universities to give me feedback. How is the best way to write such a request? First, what should I write in the email subject box? Then, how do I write the body of email?
Professors are busy people. If you send a random professor with whom you've never had any contact a paper and ask him or her to review it and provide feedback, odds are that you will never hear back from them, because they will ignore the request.
If you want a better response, you will need to cultivate a relationship with the faculty members over a period of time.
If you are new in research career and hasn't had enough relationship to be welcomed to ask for feedback, then your manuscript will likely be perceived to have low quality by busy people. In my experience you should ask it on a forum (Stack Exchange or Reddit), because your level is perfectly suited to ask there. In general, a quality post is not a wall-length post with a question "what do you think", but a post clearly explains an entanglement you found, because who can see that are indeed serious with it.
In my observation, Stack Exchange is best to ask for solution, Reddit is best for giving solution.