For something like a drink, I generally bruise the mint and use the whole leaves fresh - rub it between your fingers a bit to release the oils and then just drop it in the drink. The main benefit of this method for me is that a bunch of dry, crumbled mint in a drink is going to make it look very muddled and hard to drink, as you're constantly getting a mouthful of dried leaves (you could get around this by steeping it with the dried herbs and then straining it, but that's too much work!). As a bonus, fresh picked herbs in a nice glass of lemonade, for example, just looks so fresh and tasty!
If I'm cooking with it and I have a supply of fresh on hand, I prefer to use that. Depending on the dish, it might be whole leaves, but more likely chopped - I actually use kitchen scissors for a lot of fresh herb preparation as it can be easier than a knife in many cases.
You certainly can dry it, especially at the end of season when you need to harvest, and use the dried leaves in place of fresh. The main benefit to drying is that it stores really well; dry also seems to be a bit more powerful, at least when first dried. Over time the flavor of dried herbs will degrade. You usually use a 3 to 1 ratio replacement - if a dish calls for 1 tablespoon of fresh mint, you'd use 1 teaspoon of dried, though as the dried herbs age you'll have to increase the amount used over time.
The easy way: Use raspberry oil (preferably) or a raspberry extract in place of the peppermint oil.
The (probably) much better way: Leave out the oil and food coloring and use raspberry puree as you suggested. Strain frozen or fresh raspberries through a fine strainer or cheese cloth. Weigh the resulting juice/puree and then put it on the stove an cook it until the puree is half of its original weight (roughly). This reduced puree will be more intensely raspberry, so it will get all of the raspberry flavor without having to add as much water to the recipe. You'll have to experiment with the amount of reduced raspberry puree to use.
I wouldn't increase the corn syrup, but you certainly could if you want them sweeter. I would personally go for the opposite effect and add a small amount of lemon juice to the raspberry puree to give a little tartness to complement the sweetness of the marshmallow.
As far as the chocolate, I would recommend a darker chocolate. 55% is quite sweet, especially around a marshmallow. You should also consider the type of chocolate. Cocoa percentage isn't everything in dark chocolate. Experiment with different types of chocolate and see what fits well with the marshmallows. Just like wine, chocolate should be paired with other foods according to the subtleties of the taste of the individual chocolate.
Best Answer
Peppermint is a hybrid breed of two plants belonging to the mint genus, spearmint and watermint. In my experience, when 'mint' is referred to by itself without any other descriptors, it usually refers to the spearmint flavour people are used to (from things like green restaurant mint candies, toothpaste, etc). Peppermint will be denoted as peppermint. However, as mentioned in the comments, this may vary based on region.
There is a significant difference in taste between peppermint and spearmint; I find peppermint to have a much more intense flavour. Scientifically, peppermint gets its flavour from its high menthol content, whereas as spearmint owes its flavour to the compound L-carvone. Substitution will not replicate the same flavour as the original.
Source for science related parts: https://en.wikipedia.org/wiki/Mentha