  We study a two dimensional spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet in a
square lattice using the linearized spin wave theory recognizing the
4-sublattice nature of the underlying magnetic lattice. Multiple magnon modes
with optical and acoustic branches about the stable Neel ordered and double
acoustic branches about the columnar reference states are obtained for small
and large values of $\lambda(=J_2/J_1)$ respectively. An additional uniaxial
anisotropy, for large $\lambda$, can lead to distinct spin gaps in such
systems, as also witnessed experimentally. The single hole spectral behavior in
a 2D $t-J_1-J_2$ model, for small frustration, is then calculated within the
non-crossing approximation. Our results match fairly well with exact
diagonalization results from a $4\times4$ cluster. Hole spectral features and
their evolution with $\lambda$ resulting in "water-fall"-like smooth spectral
weight transfer are discussed. Hole energy bands are identified and the
corresponding energy-shift and reduction in width with spin-frustration are
indicated.
