When we say CC here, it means third party custom content. It's items for the Sims 3 that are made by people other than Electronic Arts. Some people love it because it brings a different look to the game, but it can be risky and mess up your game. Mods can also be risky, especially if made by people who don't know quite what they're doing. I don't recommend a mod as the first thing to try, only as a last result unless you're absolutely interested in them. We have a special board for mods if you're interested.
The problem you're having could be a glitched file that may or may not be salvageable. So, you have 4 Sims and 1 pet? And nobody is pregnant? How exactly are you trying to add Sims to the household and what exactly happens to prevent it? Sorry if you've already tried to explain this part, but we need very specific information to possibly offer some help.