My profile, along with my younger brothers and cousins, have red spartans instead of the ones we use. Is this because we only played offline for the first few levels, because we do not have LE/pre-order? What could it be and how can I fix this?
It is an issue that the team are aware of and a fix is in the works 
The Little Moa is correct. We are working on this issue and hope to have a fix soon. In the meantime are you making sure to change your Spartan’s armor while in the lobby and not while actively trying to find a game in matchmaking? Note that changes take approximately 10 minutes to take effect due to caching.