Will the PNG lose quality in the PDF?
No. Its pixels are stored losslessly, so the text in a screenshot stays as sharp as it was, at every zoom the picture allows.
What happens to a transparent PNG?
The transparency goes into the PDF with the picture, so on screen and on paper the page shows through, which is white in practice. Nothing is filled in behind it first, as saving it as a JPG would.
How do I make one PDF from several screenshots?
Drop them all at once, drag them into order and save: each screenshot becomes a page of one PDF. Same as the picture keeps every page the size of its screenshot, and A4 fits each one onto paper.