A job application email is the letter with a subject line doing extra work. Put the role title and your name in the subject, keep the body to four short paragraphs, and attach the CV as a PDF.
Nearly. 'Application letter' is the more formal term, common in South Asia and for postal or email applications. 'Cover letter' is the standard term in the US and UK. The structure is the same.
One page, three or four paragraphs. Anything longer is competing with your CV instead of introducing it.
'Dear Hiring Manager' is fine. It is better than a wrong name — and worth two minutes on LinkedIn to check first.