RNS string theory: supersymmetry in open and closed strings After reading the chapter "Strings with world-sheet supersymmetry" in Becker, Becker, Schwarz book multiple times, I am still confused about the following things.
1) Open string doubt
They prove that, in order for the boundary term in the variation of the action to vanish, one has to impose EITHER Ramond condition OR Neveu-Schwarz condition, which lead to different mode expansions.
After quantization and GSO projection, they then analyse the spectrum and find that the number of bosons in NS sector is the same as the number of fermions in the R sector, in both the ground state and first excited level. They then conclude that the theory is supersymmetric.
If one has to choose only one of the two mentioned condition, how can one have both spectra? How can the theory really be supersymmetric? I would say that it is just a curious feature of the theory, but I clearly miss their point.
2) Closed string doubt
As far as I understood, type II theories are closed string theories. At page 137, they again state what happens in each "sector" in both type IIA and type IIB. If I, for example, choose the NS-NS sector (which is the same for both theories), it would seem that there are no fermions in the theory. 
What am I missing again?
 A: The ad-hoc quantization procedures for going from the classical theory of the superstring to the quantum superstring theory are just that - ad-hoc. We're not really looking at a single string with chosen boundary conditions and quantizing it in some clearly prescribed canonical fashion, we're playing around with the superstring and are trying to get to a well-defined quantum theory, one where the resulting theory on the worldsheet is conformal and which has no quantization-obstructing anomalies. In playing around with this, we find that there are these "sectors" corresponding to different boundary conditions, and we find that if we combine them in a particular fashion (which we then call grandiosely call "GSO projection"), then we get a consistent quantum theory. 
If you are bound to the ontology that we are really thinking about "actual strings" in a 10-dimensional spacetime, then you must conclude that the states of the theory in which we have the sectors combined is the theory of more than one string, with different boundary conditions for different strings. But once we have arrived at the quantum theory, there is no way back - we cannot "unquantize" this theory to arrive back at some picture of a classical string corresponding to a particular state in the quantum theory.  
If instead you view "string" theory as a theory of (supersymmetric) conformal field theories living on worldsheets, there is nothing strange about this. 
For a little bit more about the two different ontologies, see this answer of mine.
