Once again I find I do not agree with Colin's advice. It is very easy to test a planted tanks to know how many fish it is safe to add,. The first thing to realize as there is no such thing as a planted tank which does not a;so contain some number of nitrifying bacteria. Plants hose them and when you get new plants you are also getting some number of bacteria.
There are reasons for this that Colin may not be aware of as far as i can tell. In water most of the ammonia become ammonium. The higher the pH the greater the level of toxic ammonia, NH3, will be this will be. However, most of the ammonia will be in the form of ammonum, NH4, which is much less toxic. As the water bcome more acid less and less of the total ammonia will be in the NH3 form. By the time the pH is 6.0 virtually all of the ammonia is in the form of ammonium.
The bacteria prefer ammonia as NH3. However, they are also able to process ammonium but they do so way less efficiently. This is why ther is no such thing as a planted tank which contains no nitrifying bacteria at all. One the other hand, one can have a fully cycled tank with no live plants in it at all.
How much of the ammonia is handled by plants v.s. ammonia in any tank depends on the types and quantities of the plants and then whether or not ammonia can exists as NH3.
So, the above information makes if simple to know how "cycled" any planted tank mught be before one adds fish. This is donme by a a simple dose and test method. Add ammonia, with some and then test. We do not care how much of a tanks total ammonia is being handled by plants and how much by bacteria. What matters is that it is all handled as rapidly as it is produced when live animals are present.
There is one caveat. Plants, like fish, have a different tolerance for ammonia in the water. Some plants can be harmed ro killed by a 3 ppm addition of ammonia. So when it comes to doing a dose and test on a pplanted tank is is a good idea to reduce the concentration. if you want to stock moe heavily at the outset,I suggest doing a test at 2 ppm. If youare will ing to add fish amore slowly, then 1 ppm is enough.
The goal in this is to remove any guesswork and to make it possible, should want desire it, to add the most fish all at once as they can. And then there is the fact that we do not all plant out tanks with the same plants nor the total plant mass we want to add. What we do know is that the more plants we have and the faster growing they are, the more ammonia thay can handle. And the best part about the plants is when the ammonia goes in no nitrite or nitrate results. In fact most plants will use any nitrate available since we cannot add ammonia to a stocked tank.
Seriously though, looks like ammonia is ok, the nitrAtes are OK-ish, but nitrItes still too high? Those and the ammonia are the ones to worry about, right? 
