Curry is just an herb and spice blend used in many recipes. The herbs and spices used in curry are all inherently kosher for Passover, so the only problem would be if the curry is adulterated by adding wheat or flour, or if the curry is prepared using dirty implements. Blended spices (as opposed to pure spices) need to be blended under kosher supervision to be kosher. If you are asking about curried meat dishes, they are only if kosher if the meat itself is kosher, and if the dish does not involve any milk products -- note that many traditional curries do involve milk, cream, ghee or yoghurt. The curry itself, however, is not the source of trouble.
It would have to be certified kosher for Passover.
The label has to say "Kosher for Passover"
Yes, only if they are specifically certified kosher for passover. You can find kosher for Passover olives at any Jewish supermarket
It can be, it would require a valid Passover hechsher.
Yes, it can be since it is made from wine, which can be Kosher for passover if created under appropriate supervision. The bottle would require a kosher for Passover hechsher.
If you were able to find corn vinegar that is certified kosher for Passover, it would be kitniyot which means that the majority of Ashkenazi Jews would not use it.
There are kosher food companies that are now making gluten-free products Kosher for Passover and all-year-round. However, something being gluten-free has no bearing on whether or not it is Kosher or Kosher for Passover.
Arugula is an edible leaf and is kosher year round including Passover.
Yes, they must be certified kosher for Passover though.
Some kosher companies make cereals that are Kosher for Passover.
Yes, there are no restrictions on fruit for Passover.
Lamb can be kosher for Passover. However, Ashkenazi Jews traditionally do not eat lamb during Passover.