Is there a limit past which bigger textures has no effect? I have a human model with 8k textures. will reducing the textures to 2k have an impact on visuals or performance? can I get away with compressing just the specular and bump map and keep the diffuse map at full size?
Yes reducing the resolution of the textures will eventually make the pixels large enough to notice, but will improve performance.
Compressing one map and not another depends on your node setup or in a external application it's limitations, but it should be fine.