Hmmm. Sounds like an interesting bag of "stuff" you got. The fact that you have nitrates at this point give you three possibilities...
1. The nitrates are the end-product of your cycle
2. The nitrates were in your source water to start with
3. The nitrates came in with the bag of mystery stuff from the LFS
Just to be safe and know where you're at, if it was me, I'd throw an ammonia source in there and look for either ammonia/nitrites or an increase in nitrates. If you see ammonia/nitrites, then you aren't fully cycled yet. An increase in nitrates (assuming it isn't coming in from top-off water, etc) would imply the tank is cycled.
Regarding the hang-on-back filter... a protein skimmer and a HOB
filter serve two totally different functions. One doesn't replace the other. A skimmer removes dissolved organics from the water before they can break down into nitrates. A HOB
filter mechanically removes the big chunks, and can also be used as a place to put chemical filtration products like carbon, synthetic resins, etc. Many folks don't run any type of HOB
filters on their tanks, but it all depends on how you use it.