If something has no grain in it, and did not come into contact with something that had grain in it, or even if pots are hot enough, and chametz touches the pot, and the non chametz touches the pot, it might be chametz. The laws are complicated, and this is not the right place for them. Also, many have a custom not to eat legumes on Passover because their flours' are simuler to grain flour, or possibly because kernals of grain would get mixed into them, and still do sometimes.
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.
All salt is kosher unless something is added to it to make it not kosher. Like all other seasonings, the specific package must be certified kosher for Passover.
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.
Arugula is an edible leaf and is kosher year round including Passover.
Yes, they must be certified kosher for Passover though.
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.