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.
Texture size will definitely have an impact on the performance of your computer. A larger texture will use more resources, and the resources on a computer are limited.
A texture in 4K will use 4 times more resources than one in 2K, and an texture in 8K will use 4 times more resources than one in 4k... so it is quite easy to push your computer past it's limit without much effort...
Compressing doesn't help either. A compressed image has to be decompressed in blender, so even if on disk it seems smaller, once it is decompressed in blender it will use more resources.
At the end it all depends on how large the textures will be on the screen. It makes no sense to have 4k textures on objects that will only be a few pixels on the screen. Use large textures for objects that will be displayed quite large on a screen (like object that are close to the camera). 3D is a balancing act between quality, expectations and the real capabilities of your computer.