Can I change the font for the whole page, headings included?

Body text only. Open the Theme gallery, scroll to The look and pick one of the twelve families under Storefront font, then press Save the look. Headings keep the font of the theme you applied, and that is deliberate: it is what stops a font swap from flattening a design that was drawn as a whole. If you want different headings, choose a different preset; each of the fifty-seven is a matched set of colours, heading font, body font and shapes. Keep Use theme font to follow the preset.