Yes, as plantains are a fruit.
Fresh water chestnuts are fine. Canned water chestnuts require a kosher for Passover hechsher.
Yes. Fresh vegetables are all kosher for Passover, though Ashkenazi Jews do not eat certain ones, such as corn and legumes (peas, beans, etc.)
There are brands of kosher for Passover cranberry sauce. You would have to check the packaging for kashrut certification.
As capers come packed in brine, they require a kosher for Passover certification. However, because the brine used for capers has vinegar in it, it is not possible to find brands that are kosher for Passover. If you could find fresh capers, they can be eaten.
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.