I have a question though, my adapter is dual band and I noticed this router is a single band. Can these two work together ?
Dual band means your adapter works in both the 2.4 GHz and 5 GHz bands. I think the router you got only does 2.4 GHz, so your adapter will just use its 2.4 GHz band. So it will work, but you would get significantly better results of using N within the 5 GHz band. Usually the 2.4GHz band is to crowded with other people that you cannot use the 40 MHz wide channels and need to go back to the 20 MHz wide channels (to get good performance). On the 5 GHz going to 40 MHz wide channels is no problem and you will get the faster speeds of N. Without going into more detail that is the short of it.