Honestly, your spouse's story sounds very similar to mine in some ways. My NC letter was the same... full of apologies, empathy, hope... however I sent the NC letter and then deleted it so that my wife would never see it. (Big fat dumb move that I regret to this day). I too "waffled" at first and wasn't sure how I felt or what to do. My wife finding out what was going on was something I had run through in my head a hundred times, but in my mind, I pictured it similar to how it works on TV. I figured she'd get mad, cry... maybe she'd leave me, and if she did, it would be amicable and she'd realize that it was all for the best. But that's not real life. I wasn't prepared for the real feelings, the real trauma, the real devastation. My whole rose-colored view of how things would go was like a cold bucket of water to the face, and to the soul. I've never seen someone in that much pain in my entire life. I've seen death. I've seen torture. The pain in my wife's eyes made those things look like Disneyland by comparison. Still, at that point in time, I had much more compassion and empathy for the AP and myself than I did for my wife and kids. I hate to think about that, to admit that, but it's the truth I need to own.
Sometime within the first day or two after dday, my wife told me she was going out for an hour, and that I had that one hour to figure out, and commit to, what I was going to do. Either leave and go with the AP, or stay and try to fix the marriage, but she was clear that doing both wasn't going to work. That forced me to think hard and make some hard choices, but it also forced me back into reality. I realized the damage done to my wife and kids. I also started to think what life would be like if I stayed with the AP, or I went my own way. All the things I had compartmentalized, justified or excused suddenly came to the forefront and I started to feel like I had lit the fuse on a stick of dynamite and was just sitting on the stick, waiting for it to explode.
Clarity, true clarity, took time. For me, it took a LONG time, years in fact. On one hand, I stayed committed to R. I never talked to the AP again, and while I did struggle with my feelings for a few months, I never doubted that I had made the right choice to stay and work on R. That being said, while I insisted to my wife that I loved her, the truth is, I was so very fucked up in the head and the heart that I really was not capable of understanding love. Everything about me was still selfish. I would write letter after letter to my wife professing my love, my commitment to her, and trying to explain to her how I was really still a good guy... but every single letter ended up being all about me, what I wanted, what I needed, and assuming that what was best for her was what I deemed best for her. So when you ask how he could possibly go from having an affair to suddenly loving you again, I would say... he can't. Not because he doesn't want to, not even because he doesn't really feel those feelings, but simply more of a "can't". It takes an enormous break with reality to justify having an affair, and even more so to live a double life full of lies and deceit and betrayal. Undoing that takes time and a ton of work, if it happens at all.
My best advice to you is simply to get as informed as possible (which you are already doing) and then make some hard decisions about what you want and what you are willing to accept while getting there. As I said, it took me years. My wife chose to stay, even through all the pain, all the horrible things I said to her, the callousness, the selfishness, the entitlement, the complete lack of empathy and compassion. But doing so did so, so much damage to her, to both of us really. In the end, that "switch flipped" for me, truly flipped, and when it did, my humanity and integrity and compassion came back too, and once that happened, progress was quick, her walls were able to start coming down, trust was able to be rebuilt, so on and so on.
I know that, at first, she stayed because of our daughter. She was 16 at the time and still had a few more years to graduate. My wife decided she wanted that to happen first, and then she would leave me. Luckily, I had one thing going for me, and that was simply that I refused to give up. I went to IC and MC, I read books, I did active research, I used every resource and every tool I could to help figure myself out, and then made strides to "fix" the broken parts that led to the affair. She saw this, she realized that I was trying (failing miserably, but trying) and that prompted her to "watch and see what happens" to some degree. When I snapped back to reality, it was easier for her to justify staying and attempting to R. We made a lot of legal decisions as well. We agreed upon a postnup where she got the lion's share of the assets if we ever split up. I signed papers ensuring that I would not get any of her 401K money and that the kids would get everything. We made agreements on how finances would work if we divorced and sold the house, etc. Then it was up to me mostly, to either give her reasons to stay, or get out of her way and not be a barrier to her happiness if she decided to leave. We are 7+ years out now and in a better place... we are already exploring retirement together and have bought houses and cars and so on. The plan is to stay together, but I also know, every day, that she has every right and every reason to leave, and that I need to be sensitive and understanding of that.
You are very, VERY early into the process right now. My advice? Don't put the pressure on yourself of deciding R or D just yet unless you feel really solid about either one. Take time to process and heal. Put boundaries in place that make sense and that help you to heal and not get wrapped up in your spouse's healing. Talk to other BS's about things such as "Detaching" and doing "a 180" which are techniques to help keep you safe while allowing you to also get on with living. Insist on your WS "doing the work" and if IC is a possibility, insist on that as well. They need to understand their "why's" and how they allowed themselves to debase themselves to the point of being a cheater. Doing so is what will ultimately help make them a safer person to be around. If enough progress is made and they learn to love and respect themselves again, that when the door to true love and respect for YOU will open. BS's ask about this all the time... how to know when it is "real". My best reply is simply that "you'll know". When a baby cries, you go and comfort it, not because it benefits you in any way, not even because it's the right thing to do, but because true love kicks in and we show compassion and care and sacrifice for those we truly love. That's what your WS is missing right now, they are still just doing CYA and trying to make this pain go away. That's not love. You'll know love when you see it because you will feel "seen" and "heard" and "understood" by them, and/or you will see them throw themselves under the bus for your benefit (e.g. a parent works three jobs to send their kid to college, or in this case, maybe the WS says, "You and the kids need to be safe and taken care of, so you take the house and car, I'll figure my own way to survive"). You can't cheat and have empathy at the same time, ya know?
Good luck, I hope things work out for you.