I downloaded the mod and the fabric Api but idk if the mod makes the skin of the zombies like the pictures. I'm asking if the mod can change the zombie's skin to look like the image because mine look like the regular zombies.

You need to install the following mod:
https://www.curseforge.com/minecraft/mc-mods/entity-texture-features-fabric
and the following resource pack:
https://www.curseforge.com/minecraft/texture-packs/tissous-zombie-pack-optifine-1-7x-1-20
(don't forget to enable the resource pack in game ;)