How could I get NodeType information from within a controller? E.g., for checking access rights?
I'm not sure if that's what you are asking for:
You can get access of a nodes property within a controller (e.g. for an extension) like this:
$myOwnProperty = $this->request->getInternalArgument('__myOwnProperty');
"myOwnProperty" has to be defined for a nodetype in Configuration\Settings.yaml
The internal argument gets two underscores before the property name.