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LOL Wookie - you are on a mission! Sounds yummy but I hope you can share with friends or co-workers.

I've never frozen cream cheese icing but cheesecake (which is largely cream cheese) is one of the best cakes to freeze. I'd give it a go just securely wrap it to prevent strong odors from penetrating. Wrap once in plastic and I'd also wrap in foil. Let come to room temp (or just below) and re-whip to use.

As for the lace cookies, my suggestion would be to freeze the extra dough. Lace cookies are so delicate, I think they'd be best done fresh (even from frozen dough).

I think in general freezing the cookie dough works the best. I've found that those glossy plastic bags that cereal comes in to be good for wrapping cookie dough to be frozen. It's tougher than wax paper and peels off the frozen hunk easily. I cut open the bags into a flat sheet. Wrap the dough. Then seal it in something airtight.

I have no idea about if the frosting will freeze. I usually don't frost my carrot cakes.

Frosting after you freeze you have to bring to room temp and possibly whip it again with a tsp or 2 of milk.
wraqp your cake well. I wrap mine in wax paper and then plastic wrap like a mummy. Cookies I form and freeze then put in a zip bag.

Slightly off topic but along the same line: muffin batter freezes surprisingly well. Works best if you can portion it into tins, then freeze. If you freeze it in the bowl it will still work, but you have to wait until it thaws to scoop it. We did this in culinary school and I think the muffins turned out even more moist than if we had used freshly made batter.

I've frozen buttercream icing with success but never cream cheese. I would think the cream cheese would break down once it thawed.