It is fine as long as it isn't a solid rock, then you need a hammer to break it apart. However if it is hydroscopic like some I've used, you might have a wet mess that is a pain to try to apply, and could even be health threatening if you get too much of that liquid on your skin at once.
Yes you can spread it this time of year, but it is a bit of a waste to do so now because the lawn won't make much use of it now that DC winter is upon you, much will rinse away with rain and snow. You might as well sit on it till spring, or if any is calcium chloride, use that to melt ice.
The spikes, you may find that they crumble when you try to drive them in the ground. You might want a wooden or metal stake to make a hole to drop them in.