No. They are made from oats, which is one of the "five species" of grains that are traditionally banned for Jews during Passover (Exodus ch.12).
There are "Kosher for Passover" dry cereals similar to Cheerios that are made from matzoh meal, but I've tried them so you don't have to. Stick with scrambled eggs; they're better for you.
60+ years ago, a very young chemist named Isaac Asimov wrote a Science Fiction story about a powder that would dissolve 1.2 seconds BEFORE you added water; he called it "thiotimoline". Matzoh Cheerios are very much like that.
The Cheerios box I have in front of me is Kosher, certified by the Orthodox Union -- their certifying mark (heksher) is an O with a small U inside. Look for that mark on the box. I have seen Cheerios boxes without a heksher, leading me to conclude that some production lines are under kosher supervision and some are not.
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.