We argue that Raman study of Fe-pnictides is a way to unambiguously distinguish between various superconducting gaps proposed for these materials. We show that $A_{1g}$ Raman intensity has a true resonance peak below $2Delta$ for extended s-wave supe
rconducting gap, $Delta(mathbf{k}) = Delta (cos k_x + cos k_y)/2$ in the folded Brillouin zone. No such peak emerges for a pure s-wave gap, a d-wave gap, and another extended s-wave gap with $Delta(mathbf{k}) = Delta cos{frac{k_x}{2}} cos{frac{k_y}{2}}$ proposed by several groups.
We analyze antiferromagnetism and superconductivity in novel $Fe-$based superconductors within the itinerant model of small electron and hole pockets near $(0,0)$ and $(pi,pi)$. We argue that the effective interactions in both channels logarithmicall
y flow towards the same values at low energies, {it i.e.}, antiferromagnetism and superconductivity must be treated on equal footings. The magnetic instability comes first for equal sizes of the two pockets, but looses to superconductivity upon doping. The superconducting gap has no nodes, but changes sign between the two Fermi surfaces (extended s-wave symmetry). We argue that the $T$ dependencies of the spin susceptibility and NMR relaxation rate for such state are exponential only at very low $T$, and can be well fitted by power-laws over a wide $T$ range below $T_c$.
