Re: Is he Cheating? Texting.
Sorry, but it's the behavior of someone hiding things from you, and clearly he has inappropriate dealings with other women. Also, if he's discussing your marital details with another woman, he's at least in an emotional affair, quite possibly physical since they're alone at work all the time.
What kind of phone does he have? If it's an iPhone you can recover his recent texts (deleted or not) from the computer he syncs with - there's a backup file. (there are ways with other phones too) Then you can see exactly what they've been texting and make up your mind based on the truth.
Definitely red flag behavior, the people here will give you lots of good advice...