Welcome to SI and so sorry that you're here. Have you been to the JFO (Just Found Out) forum? There are some pinned posts that we recommend to newly BSs (betrayed spouses) there. The Healing Library is at the top of the site and has a lot of great information.
As for IC (individual counseling), it can be very beneficial. Betrayal trauma is horrible, and you will need to heal from this. There are members who have PTSD or C-PTSD from what their partners have done to them. (I had PTSD.) This really is no joke.
The obsessing is the effect of trauma on your brain. The sad thing is, your brain doesn't know the difference between a lion chasing you down to eat you and your intimate partner betraying you. Give yourself a lot of grace and practice self-care at this time.
For me, I wasn't able to concentrate for more than 15-30 minutes for close to 2 years. What helped me was doing mindfulness exercises and learning meditation. The meditation exercises helped me to realize when my thoughts were spiraling, do some breathing and bring my focus back to where I needed.
You have every right to not believe what he's doing or saying. He hasn't built trust and doesn't seem remorseful. If you can, treat him like a very bad flat mate and you're waiting for the end of the lease to get out.
Your daughter probably suspects that something is wrong, and may think she's the problem. Kids are smarter and pick up on things and we don't give credit to them for doing so.
Go see a barister (or several) to get an idea of what divorce will look like in your scenario. This will give you knowledge, and knowledge is power.
On his dark thoughts...well, that's his responsibility. If he does anything to act on those thoughts, call the authorities. They're equipped to handle those situations. It isn't your responsibility. I mean, think about it. What can you do? Not much. It may be a manipulation tactic that he's using to control you, or it can be that he really needs professional help. Figuring out which one it is? That isn't your responsibility.
Again, I'm so sorry that you're here.