This "small set of direct questions," in my opinion, is implicit in the job description/duties and desired qualifications. Employers lately have had challenges in job definition, of course (they seem interested in advertising for the company rather than a job, and the job descriptions have become increasingly elastic; in their defense, retention is hard, and it can be difficult to slot people into single roles anymore).
My general practice in responding to job postings is to prepend my resume with a table containing the job requirements vs. my experience with an estimation of whether I meet the requirement (check, dash, X) and a brief explanation.
In cases where there aren't any job postings, but I have an interest in the company—or if I want to make an impression that I'm targeting them—I'll send a cover letter by postal mail with a printed resume. Usually it's a few sentences: here's why I'm interested, how I might be useful to you, and here's a resume with contact information if you want to reach out.