A speculative letter to a company with no open role needs a reason for existing: something specific about their work that you can contribute to. Name it in the first two lines or the letter gets deleted.
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.