A job application letter is the formal cover note sent with your CV, common where applications go by post or email rather than through a portal. It names the role and where you saw it, gives three or four sentences of directly relevant evidence, and asks for an interview — the CV carries the detail, so this stays short.
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.