I am keeping my Ammonia Levels around 5ppm at least until I see Nitrites. I should start seeing Nitrite levels but instead I am only seeing Nitrate levels starting to rise. It is still in the safe range but shouldn't I be seeing some Nitrites first????

your ammo should have dropped to 0 along with nitrite before seeing nitrate (but of course you knew that part) however I'm not sure what the results would be if you have continued over the course of 3 weeks to physically add ammonia. The concentration from that bottle of ammo you're creating is probably more of a spike (When added) then would normally be gradually "peed" out by fish.. I would stop adding the ammo for a few days and see if your nitrate levels hold or increase.

I know that 5ppm is what many sites suggest, but according to my experience, this is way too high. I always think that 1-3ppm (for heavy stocking) is the way to go.
You are doing fine. When the nitrite starts to rise, you should not decrease the ammonia you feed the system because your nitrosomonas will starve. You should keep feeding them daily. Practically, when nitrite spikes, you will see that even if you add the right ammount of ammonia to maintain your original (pre-nitrite) levels, the bacteria will consume all of the ammonia overnight and every morning you will be getting 0 readings of ammonia.