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Write the content in Markdown and let the layout be someone else's problem. The result is a PDF with a real text layer — which is exactly what an applicant tracking system needs in order to read it.
A résumé is mostly a short list of headings, dates and bullets, and almost all the time spent on one in a word processor goes into fighting the layout rather than improving the content. In Markdown the structure is unambiguous, the file is small enough to keep in version control, and tailoring it for a specific role is a text edit rather than a formatting exercise.
Most large employers parse your PDF before a person sees it, and most parsing failures come down to the file not containing readable text in a sensible order. A few choices matter more than the rest.
The style panel is the fastest way to gain or lose a page without cutting content you wanted to keep. Reduce the margins, drop the body size by a point, and choose a more compact typeface — Inter and Source Serif set tighter than Merriweather at the same size. Turn page numbers off, since a one-page résumé does not need one, and leave the title page off so your name stays at the top of the first page.
Name as the top-level heading, contact details on the line beneath, then one second-level heading per section — Experience, Education, Skills. Under each role, a third-level heading with the job title and dates, then bullets for what you actually did. Nothing more elaborate is needed, and anything more elaborate is where parsers start guessing.
Yes, provided the PDF contains real text rather than an image. This converter produces embedded, selectable text with a sensible reading order, which is what parsers need.
Narrow the margins, drop the body size a point, and pick a more compact typeface in the style panel. The preview shows the page count as you change them, so you can stop as soon as it fits.
Yes, if you write them as Markdown links. They stay live in the PDF, so a reviewer can follow them straight from the file.