Can Stil be used, as in English, to mean both (1) fashion/style, and (2) the manner/way/approach one does things?
Yes. Originally "stilus" means "instrument for writing", then "style of writing". The other meanings derived from that.
They say it wrong, its not pronounced with an "sh" sound, just with "s", same as the beginning of style
Why isnt 'mein', 'meinen' in this? It is der Stil. doesnt that make the ending become 'en'
war is a form of the verb sein, so Stil is still the subject and is in nominative.