Hi Vicki, the rocks will take around 6 weeks to cycle.
In the mean time it is very likely the seahorses will suffer & possible die. As you're 3 hours from the shop it may not be possible to return them, but if you have a source of seawater you could keep them in a different container & do a 100% water change each day, just ensure the container is well aerated.
To test when the rocks are cycled, for the first 2 weeks or thereabouts you will have ammonia in the water, then ammonia will subside as it is changed into nitrite. It will take around another 4 weeks for nitrite to subside as it is converted to nitrate. Once the nitrite is gone it will be safe for your seahorses. You should then monitor nitrate periodically, I'm not sure how much seahorses can tolerate but just make sure it's at a safe level for them.
The brown crud on your rocks - hate to tell you this but unless you get a protein skimmer it is likely you will always have algae etc growing. BTW vodka can be effective, but ONLY if you have a skimmer. No skimmer, no point dosing vodka.