Zombie's only come at night, and if they are in daylight they will die because they do not like light, they only like dark and they only spawn in dark spaces. They will attack you and follow you if they see you or if you go near it. They can be diffrent zombies like the villager zombie.
They will be made if a zombie will attack them. They can be cured if you want to see how to cure him Click on this video: From: Humily Nation
About Small Zombies:
Small zombies can have armor and i forgot to mention that normal zombies and villager zombies can also have armor, you can make them have small armor if you make them not move around so much and just throw the armor you chose at them and boom the armor is on. Small zombies are also like normal zombies, but much faster. So you better be carful with them. By the way, if your putting armor on a small zombie it may look weird like...