Should I remove the skins from the raw almonds before I grind them up and add them to the mix?
And can I use Blue Agave Syrup instead of the corn syrup?
The cookies would probably look nicer if you remove the almond skins. It is easy enough to do--just let the almonds sit in boiling water for a minute or so and pop the skins off. it's actually rather fun and can induce a Zen state. Be sure to completely and totally dry off the almonds before you use for the cookies.
Almonds with skins won't ruin the cookies--perhaps they may add a tone of bitterness, but it shouldn't be overpowering.
As for the agave syrup, I think it is sweeter than corn syrup, so you might need less. I suspect it might also change the texture of the cookie.
PS A good rule in baking is to follow the recipe and not make substitutions for major ingredients like flour, sugar and eggs. If you have some experience and understand your ingredients, then you can play around, but don't expect perfection on your first or second efforts. If you like to improvise, read some books that focus on the scientific approach to cooking. Harold McGee and Shirley Corriher are good sources.
I agree with M on everything except the almond skins. I make these with skin-on almonds as i do for everything i make with almonds except almond paste. No bitterness and the flecks of brown are attractive in any cookie.