From what you described it sounds like the tank just finished cycling. In a sterile tank ammonia builds up, then one bacteria gets established and the ammonia breaks down to nitrite, then the second bacteria gets established and you see nitrate. If youve seen nitrite, and now nitrate then the cycle has basically run it's course and the fish ought to be ok, nitrate won't hurt them.
My only concern is that it sounds like the nitrate went from 0 to 10ppm overnight after doing a water change. I would check the source water and be sure it isn't the source of the nitrate. Assuming the nitrate is being produced in the tank you should be ok. Another water change wouldn't hurt but don't do it in such a hurry that you don't have the chance to mix and aerate the new water properly.
("What confuses me is that when I read up on Ich is that after the parasite falls off the fish it seems as if there is only 4 days before it can find a fish and if it doesn't then it dies or becomes dormant. So why are you suppossed to wait 4 weeks before reintroducing fish back into the infected tank?")
I don't remember the correct terms but there are 3 stages. On fish, dropped cysts, free floating looking for a fish to latch onto. The dropped cysts can lie dormant for 4-6 weeks or possibly more. once they hatch out, the free floating stage is a few days then they die if they don't find a host. That's why the display needs to be fishless for 6-8 weeks. The cysts can hatch out in a few days or over a month.
Also keep in mind that Ick treatment is a commonly debated subject. Some people argue that it's at least dormant in most tanks and can't truely be eradicated (take this as saying that the cysts can lie dormant for far longer than 6 weeks). Others argue that it can be eradicated if treated properly. Personally I just finished an 8 week quarentine and hypo treatment. Fish have been back in the display for about a month. I saw what could have been a couple of spots on my tang a day or two ago. If I am seeing a reinfection I'm pissed, and a bit more inclined to believe that Ick can lie dormant for longer than 8 weeks.