Install drupal without node module? I know this is achievable in Drupal 8 but is there a way to do this in Drupal 7? I've looked into drupal modules, core files but couldn't find anything reliable. I'm asking this because I might want to have a light installation with custom entities and I don't need Node module.
The node module is marked as

required = TRUE


in the node.info file, so the developers are basically saying that as far as they're concerned the node module is imperative for Drupal 7 to function correctly.

You could try patching the info file to remove that line, then disabling the node module to see what happens...in fact if you do that you should write a blog post about it or something, it would be very interesting to find out the effects; I've never heard of anyone trying to do this before :)