No processed food is kosher for Passover unless its label has a symbol of reliable Rabbinic supervision.
Agave is just a green vegetable, so its refined juice is in the same category as maple syrup. Entirely acceptable.
The majority of sweetened condensed milks are made with corn syrup and are not certified kosher for Passover. There are substitution recipes though.
There are kosher brands of condensed milk, to be used during Passover, it would have to be certified kosher for Passover. In regard to sweetened condensed milk, most use corn syrup which is kitniyot. There are substitute recipes for this product though.
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, during the passover season the Cokes labeled "kosher for passover" have different ingredients. The regular coke uses sugar rather than corn syrup and the diet coke uses a specific type of aspartame that has been deemed "kosher for passover"
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.