Specify a custom sharing image for Facebook. You can upload an image, use the first image in the post, or use the post thumbnail.
Uncheck the appropriate box in the panel on the post editing screen.
Because that's what I'm used to using. If you can tell me why I should use
<meta property="og:image" content="…" />, I'm totally open to change.
Probably, yeah. I might add a setting to always add a default sharing image you can set, if none of the other options are checked.