Lamb can be kosher for Passover. However, Ashkenazi Jews traditionally do not eat lamb during Passover.
No. You should eat lamb instead
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
Killing and/or eating lamb during passover is actually not done by Ashkenazi Jewish custom. Many Sephardim do eat lamb during Passover with some Ashkenazi Jews starting to eat lamb too. Due to the religious laws surrounding kosher slaughter, not anyone can slaughter an animal for consumption. Specially trained people called a Shochet are the only ones allowed to do kosher slaughter.
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.