1. 'Originate' means 'come from'. The vegetable orginated in Italy, not 'was originated'.
2. I don't think the description 'package of disease fighters' is appropriate. The vegetable contain certain substances/nutrients which can fight diseases but that is only one aspect of and not everything there is about the vegetable. You can say 'it is packed with/rich in 'disease fighters' '.
3 & 4. Just as you have used 'cholesterol-reducing' as a hypenated word, anti-viral & anti-cancer are also hyphenated words.
'Anti-viral activity' could be replaced with 'anti-viral properties'.
not a teacher