1 It might help learners to know a few names, but they will naturally come across them in texts, etc. It could be useful to know the gender of some names, but I wouldn't teach names. Names of products are part of vocabulary- you need to know Big Mac to order one. However, I don't think I'd bother counting the number of names someone knew as part of their vocab if I were trying to work out how many words they knew.
2 I don't see much difference in the meaning of neutral there. It's work modifed by an adjective to describe it- the adjective could be replaced by many others.