It depends - if you are of Sephardic descent - from Spain, Portugal or North Africa - then yes. If you're from an Ashkenazi background - the rest of Europe - then lentils fall into the category of kitniyot, small things, which have traditionally not been eating during Passover. This tradition stems from the fact that flour can be made from kitniyot, which increases your chances of accidentally consuming chametz or may cause others to believe you are consuming chametz. However, although this tradition has been upheld for many centuries and is supported by most rabbis, it is not based on the Torah and as such many Jews do eat kitniyot during Passover - not least of all because so many people are vegetarian or vegan, and kitniyot are an important source of protein.
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.
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.
Some kosher companies make cereals that are Kosher for Passover.