Some minor changes in recipe: Is it okay to use carrot marmalade instead of orange?

The almonds are pretty much the whole cookie. They get ground up and provide all the bulk and some structure. You could substitute a different kind of nut, though it'll obviously change the flavor and may affect texture too, since different nuts have different hardnesses and different amounts of oil. But leaving them out isn't possible.

The lemon zest is fine, just a different flavor.

And carrot marmalade... again, different flavor, but as long as it's the same sweetness and not any wetter than the orange marmalade it should work. I don't think it'll be as good, personally, though, this recipe is going for a nice strong orange flavor.

I like that recipe a lot and it's fun to do. As Jefromi said in his answer, skipping the almonds is not an option. I plan to try it using hazelnuts (peeled, blanched and lightly toasted) as a substitute, but it's a very fussy recipe so it may not work. As far as the zest and the marmalade, as written the recipe is going for quite a bit of orange flavor. I didn't actually want that, I was serving the cookies with a butterscotch pudding and it seemed like the orange would clash. I used apricot/peach preserves instead of marmalade and got just the flavor I was hoping for. You do want to be sure that any substitution you make for the marmalade has plenty of sugar and pectin. The zest is just for flavor, so you can skip it if you want.

Just FYI, my first batch of cookies burned. Watch them carefully, you may need to remove them from the oven much earlier than it says in the recipe. I also wound up using a much lower oven.