The copods are tricky little things. I saw thousands of them when my tank was 2 weeks old to about 2 months old. Now that I have added a few fish and some corals I don't see them anymore. I don't see them at night either. One way to try to spot them better is with a red light instead of just a regular flash light. They don't run from that and you may find other interesting things besides pods. I've found a few things this way but still no pods. I don't know if one of my fish is eating them or if they died off because of them no longer having food. I hear they fluctuate with how much dead stuff you have in your tank. If you have a lot of dead things (like curing live rock) your probably bound to see a lot more than if everything is going good. If you started with already cured rock you may have to jump start your system with adding some. I don't know how well this works though. If you don't plan on keeping anything that is dependant upon them like sea horses or a mandarin fish I wouldn't advise adding them to the tank. You may throw off your levels by doing so.
Now about your nitrates. Have you tested the water you are using for your water changes? Also there is a small possiblility that your salt mix may have some depending on the brand. Check both of these for the first places. How long has the tank been cycling? Is this a new tank or an established tank? If new it may be part of the cycle and just needs time to come back down. If you are really concerned about it there is nothing wrong with doing a larger water change up to 50% to get a change. However, if you have sensitive corals in there be careful!!! This is much easier done on a fish only tank. You must make sure that everything is exact including temp, salinity, ph, calcium and alk. Also make sure that you are ageing your salt water for at least a day. This made a difference for me. Hope it gives you something to go on.
Angie