Perhaps a male perspective would help.
As odd as this may seem, this is often a males way of trying to make amends. Men usually show remorse by opening up much more than they normally would. By allowing you access to his phone, computer and so on...and by being transparent, I believe he is trying to show you that he is worth trusting again.
Would I trust him fully? No, not really. He cheated and that will take time to repair and to heal. He has a lot of your pain and hurt to deal with and it is expected that words alone are not going to be enough. However, it seems that he is off to a good start and this, while I would still be very cautious, looks genuine. Steven