2) "Against" - I would use "for"
3) "May" - that's fine.
My version of your letter would probably be: "I am seeking an opportunity to join a company which can benefit from my expertise. Your company stands out to me as an excellent potential employer.
I have, therefore, attached my CV for your perusal. Please consider me for any entry-level positions/vacancies you may have now or in the near future.
Thank you for your attention.
Student or Learner