Okay, right now your whole world is collapsing and you are desperate for answers. Unless you are patient and methodical, you will never get them. The best case scenario is that someone else has stolen your partner's details to cover up their real identity. This is possible if the photo is not of him.
The worst case in this situation is probably that he is looking for phone sex and the like. If he was looking for hookups, he wouldn't use a fake picture. (By all means you can do a simple test though. Keep a record of his car mileometer. When he says he is going somewhere, check how far it is to go there and back. If the mileage is significantly different you will know he is lying, without having to do anything too invasive to his privacy).
What you need to do is try and hide your feelings and observe him. Is his behaviour different? Classic signs are spending more time in the bathroom, going to bed early or late and being short tempered. Also, you will find cheats are terrible at covering their tracks. You won't necessarily find out exactly what they are doing but you will be able to catch them in a lie sooner or later.
One other thing. Good people often expect cheats to confess their sins when they are found out. Man or woman, they almost never do. They will only ever admit to what you know, at most, and they will try and explain that away too. They mind even try angling to find out what you know. If you catch them red handed, they will almost certainly blame their behaviour on you. It is all bollocks and for your own mental health you can safely ignore it. A cheat's brain is so warped you would be as well to get fashion tips from a 3 year old.