A series of high quality BaFe$_{2-x}$Ni$_x$As$_2$ pnictide superconductors were studied using magnetic relaxation and isothermal magnetic measurements in order to study the second magnetization peak (SMP) and critical current behaviour in Ni-doped 122 family. The temperature dependence of the magnetic relaxation rate suggests a pinning crossover, whereas, it's magnetic field dependence hints a vortex-lattice structural phase-transition. The activation energy ($U$) estimated using the magnetic relaxation data was analyzed in detail for slightly-underdoped, slightly-overdoped and an overdoped samples, using Maley's method and collective creep theory. Our results confirm that the SMP in these samples is due to the collective (elastic) to plastic creep crossover as has been observed for the other members of 122-family. In addition, we also investigated the doping dependence of the critical current density ($J_c$) and the vortex-pinning behaviour in these compounds. The observed $J_c$ is higher than the threshold limit (10$^5$ A/cm$^2$) considered for the technological potential and even greater than 1 MA/cm$^2$ for slightly underdoped Ni-content, x = 0.092 sample. The pinning characteristics were analyzed in terms of the models developed by Dew-Hughes and Griessen $et$ $al$, which suggest the dominant role of $\delta l$-type pinning.