Learn English – What’s the meaning of ‘smile and shake his/her head’

As in any language, English writers are going to make up metaphors that are not common idiomatic expressions. In this case "pull up her smile" suggests she's forcibly lifting the corners of her mouth into a smile, even though she doesn't feel like smiling at all.

If you can't find an expression in the dictionary or by searching online, assume it's something the writer made up and use the context to figure out what is meant -- the same as any native speaker would do. Make an "educated guess" and see if it fits.

I am not too familiar with Hegel or Marx, but the usual meaning in a context like this, is that Marx took Hegel's ideas and used them to reach a completely opposite conclusion. In this sense, Hegel's ideas were overturned, just as if he were literally standing on his head.