lets see if i can answer some of these questions for you
fiji (not figi) is a location from which the LR comes...theoretically if it came from an established tank then it is cured (meaning die of has occured and there is a viable population of live critters), though you may have had some die off during transport and the addition of it to your tank which means it needs a short curing time. in short, the LR should be fine
I would, as sam suggested, wait to buy anything new for a couple weeks and continue to do some testing. the snails and crabs will serve as janitors for your tank eventually, but they won't do anything but mess up your water if they are dead. nothing you can get will "clean up in order to lower my nitrites" you just have to wait it out for the LR to finish curing. I find it odd that you say your nitrates test zero but your nitrites are high. first of all, the presence of nitrites makes a nitrate test innacurate, but nitrates will generaly read high when there is nitrite in the system
there is no reason to use your air bar...for some reason people seem to believe there is value in these things but they really do nothing for you
a powerhead is definitely not the same as a skimmer. a powerhead circulates water, a skimmer pulls nutrients out of the water...for your ten it is going to be hard to find a skimmer other than a HOB kind. if you decide you want one, the aquac remora is a good hob skimmer and i know that wayne is using the red sea prizm with success.
the power filter should be fine for creating some water circulation (essentially using it as a powerhead) and running some carbon on occasion, but generally speaking you aren't going to want to run it with the filter media in it.
i hope this helps some; what will really help, though, is getting a good book and reading some of the other posts here...there is a lot of information which it is impossible for us to cover without writing a small novel...which i reckon we could then sell, but somehow it seems the information is already out there
at this point, here is what i would do:
1)Let the LR sit in the tank with the filter running (no cartridge) and wait for your water parameters to stabilise
2)Meanwhile, read Palleta's New Marine Aquarium and read up on this website, especially the sticky at the top of this section about setting up a new tank
3)Wait some more...and get used to it; also realize that you will spend about as much on this 10 as you would likely spend on a 35 to 55 gallon tank and consider getting something bigger...
4)Wait some more and realize this is a slow process; decide whether you want to keep corals, and what kind (this may require a lighting upgrade)
5)while waiting some more, consider what fish you want to keep given that one is probably going to be the most you can keep in a tank of this size
6)Did I mention this is a slow process? Wait some more and do more research about fish, inverts, etc; at some point along the line here you should probably experience an algae bloom
7)Add a cleanup crew, and, you guessed it, wait some more
8)Add a fish and enjoy your weekly water changes
