All vegan marshmallows - which contain no animal products and as such are parve - are kosher so long as they are kosher certified. The majority of kosher marshmallows on the market are made from fish gelatin which are also parve. Please see the related link for some brands of kosher marshmallows.
Kosher cookies are cookies that have been made with kosher ingredients. For example, no gelatin from animal sources (so marshmallows must be kosher, which are made with fish or seaweed-based gelatin.)
Usually gelatin. Kosher marshmallows are made either with fish gelatin, or with Kolatin™ brand kosher gelatin, which is made from the bones of kosher slaughtered cows.
Most of the kosher stores sell kosher marshmallows, such as Elyon, and also in areas with very large Jewish populations there are chain supermarkets that have huge kosher sections, and they will be in that section. But there are no ordinary non-kosher stores, or ordinary supermarkets with only small kosher sections, that sell this. Ordinary marshmallows are all treif, because of the gelatin.
Non-kosher pickles usually have the same ingredients that kosher pickles do only they're not made under kosher supervision and the ingredients used (vinegar mainly) might not be kosher.
No, the ingredients are not Kosher.
No. From what it says, there is Gelatin.
It can be if it's made with kosher ingredients in a kosher kitchen.
No. Almost nothing with marshmallows is kosher, due to the gelatin. Packages of kosher marshmallows are an exception to the rule, of course, so it's entirely reasonable to add your own (kosher) marshmallows to kosher hot chocolate.
There does not seem to be any brand of marshmallows with that name.
It could be made with non-kosher ingredients.
It needs to be cooked in a kosher vessel and have kosher ingredients. If purchased, it (or the bakery) should have kosher-certification.