  In this work we present the results of the bulk magnetization measurements in
a superconducting state of single crystals of
Ba$_{0.65}$Na$_{0.35}$Fe$_2$As$_2$. The isothermal magnetic field ($H||c$ axis)
dependent magnetization ($M$) loops exhibit a second peak (SP) or `fishtail
effect', as well as remarkable flux jumps at low temperatures. The critical
current density $J_c$ obtained from the $M(H)$ loops is rather high, of the
order of 10$^6$ A/cm$^2$. The analysis of the temperature and field dependent
$J_c$ implies that high $J_c$ is mainly due to collective (weak) pinning of
vortices by dense microscopic point defects with some contribution from a
strong pinning mechanism. Pronounced magnetic instabilities in terms of flux
jumps depend strongly on temperature as well on the field sweep rate. The field
for first flux jump as calculated from an adiabatic model, however, is much
lower than the experimentally observed values, and this enhanced stability is
attributed to a flux creep phenomenon. The analysis of field dependent magnetic
relaxation data additionally supports a collective pinning model. The data
further suggests that SP in M(H) is likely related to crossover in creep
dynamics from elastic to plastic mechanism. We have constructed the vortex
phase diagram on field-temperature plane.
