He is an a$$hole. Sorry, but if it were me I'd be calling time on your marriage. There's A LOT of lying, and if the events were isolated I would think it would be salvageable, but there is way too much distrust.
To answer your question I am happy for my husband to have female friends and I trust him implicitly, but I wouldn't if I read those messages between him and other women, they are totally inappropriate and don't come from someone who is happy in their marriage. Depression is a hard thing to deal with but if we doesn't want help then you can't make him, and TBH it doesn't sound like he wants help. He is having everything done for him and there is little reason to change.
I honestly believe you need to separate, even as a trial, it might give him the kick up the bum he needs. If it doesn't, you know the marriage was going to end anyway - 8 years is a long time to be unhappy.