Thanks for your nice complement about the picture. That is me in younger days at my physical and mental peak. My old friend and office mate from grad school just sent me that picture. I haven't seen him in 26 years, and he will be visiting from Australia in a couple of months. He took that picture while we were studying for a brutal exam in probability theory. The teacher flunked every student in the class on the midterm exam and threatened to fail every student for the course if we did not do well on the final. We were studying for days and days at that point. I was determined to do well on that exam and you may see the fire in my eyes in that picture. That final exam required every ounce of creativity and visualization I had. But, I was in the zone that day and nothing could distract me. Even my calculator battery dying just before the exam did not bother me, I just borrowed my friends calculator during the exam, which I wasn't even familiar with. I worked with perfect efficiency for 3 hours straight and calmly finished the exam one second before the Prof called the exam over. This may sound as exaggeration, but it is exactly what happened. As I walked out of the room with my friend he turned to me with a look of shock and said, "that was brutal" (no one else had finished in time), but I knew I had done well and just said, "I think I did ok". I ended up with the highest grade which gave me an A for the course. The Prof. (a well known guy in his field, who has written many text books) failed half the class for the course that year. He wasn't fooling around.
Not trying to brag because that guy in the picture is almost like a different person to me now, and this "operation in the zone" will happen to everyone at some point in their life. I was just fortunate that it came at a critical time when I needed it. But, I think there is a lesson here. If you prepare to the fullest extent of your ability and KNOW you deserve to do well, there is a sense of calm you will have when you enter the "arena". This confidence can do nothing but improve your chances of success.
Anyway, on to the questions!
Q1: There are two ways to answer this.
First, consider the formula itself. By definition E2 is the excited state, which means it has higher energy than E1, and this means E2-E1 must be positive. If T is very large, then exp(0)=1 which means that N2 is about equal to N1, but since the -(E2-E1)/kT never goes to zero, but is a very small negative number, N2/N1 is equal to a number near to but less than one, which means N2<N1.
Also, if T is small, then the exponential argument looks like exp(negative large number) which means N2/N1 ~ 0 meaning that N2<< N1.
Second, consider the physics. Thermal excitation occurs when the thermal energy KT is comparable to or greater than the energy difference E2-E1. If kT is small, there is not enough energy to cause the excitation and N2<<N1. If KT is large, then there is plenty of energy to cause excitation. This might lead you to believe that this leads to N2>N1, but if that happened, you would need an energy input to the system to maintain the population inversion. However, an energy source causing excitation is not a case of thermal equilibrium. In other words if N2 could be greater than N1, you would be able to make a laser without an input energy source and you would have free energy. So energy conservation requires N2< N1 in thermal equilibrium.
Q2: This result follows from the fact that, at most, N2 is just slightly less than N1, If N2<N1, then you have N2<Ntotal-N2 which means 2N2<Ntotal, which means N2/Ntotal< 1/2.