1) Yes, the term "fermion" is referred to particle that have half integer spin (as you said 1/2, 3/2 and so on), while "boson" is referred to particle with integer spin. This have many consequences. First of all the wave function of N fermions must be antisymmetric under exchange of any two of this N fermions, while for bosons it has to be symmetric.
2) In term of quark model a "meson" is a particle composed by a quark and an anti-quark. There are six quarks in nature and their quantum numbers are (considering only charge and strangeness):
UP (u) Q=+2/3 S=0
DOWN (d) Q=-1/3 S=0
CHARM (c) Q=+2/3 S=0
STRANGE (s) Q=-1/3 S=-1
TOP (t) Q=+2/3 S=0
BOTTOM (b) Q=-1/3 S=0
The only way to have a meson with strangeness is to include a strange or anti-strange quark in its composition. So for example, if you want a meson with S=-1 you have to put a strange quark, but for the composition of mesons, the other element must be a anti-quark and as you can see from the list there is no way you can have a total charge Q=+1. The same reasoning is valid for the other combination S=+1 Q=-1.