Thanks for your interesting questions.

Parts-of-speech are interesting categories, and like most things in language, seem to suffer from prototype effects. It looks like there is a spectrum from 'strong' category members (dog is an obvious noun) to much 'weaker' ones (like think in 'I'll have a think about that'). And occasionally we need to re-classify: thus core gained full adjectival status when it developed from a mere noun modifier ('our core values') to acquire truly adjectival characteristics ('these developments are core to the company's future'). Also, dictionaries have always used the category adverb as a bit of a fallback for anything hard to classify.

With regard to determiners and predeterminers, I don't think there is any hierarchy here. What we tend to do with any kind of 'function word' is have a box (with a red tint in the printed version) which focuses on usage, explaining the ways in which a word like both can function as a determiner, predeterminer, or pronoun, giving examples of each use (since it's unreasonable to expect that all our users will be familiar with these terms).

This seemed to us a better idea than separating these uses into different homographs (as done in many dictionaries), when all the uses convey the same semantic information.