I so empathize with you and the absolute desperate feeling you have to save your marriage, and really relate to the not "needing", but wanting. It's the only thing I want in my sitch as well. It shows our true commitment to another person.
The only thing I can offer in terms of the "why" for what your husband is doing in offering to help with bills, etc. is guilt. My H would do things that seemed to be wishy-washy to me too, but when I'd point out that it seemed like he wasn't sure, he'd become adamant that he was sure and nothing had changed on his end. Then he'd continue to act like he would come to the house every so often to help out with things like taking care of the yard.... I had to tell him very bluntly that it made no sense for him to tell me he doesn't want to be with me, but yet wants to be my lawn man?! And the only reason is because it made HIM feel better about himself given the other ways he was hurting me.
But, I obviously can't predict why your H is doing this. It does sound like your H's behavior is much more on the fence than mine has ever been, and ever since I told my H I didn't want him in the house, we have been pretty much completely NC. I did have to ASK my H finally if he could give me money for things I'm still paying for like car insurance, health insurance, etc. and he agreed to transfer the money to me each month (we will see if it happens) "until" there's a divorce decree. Yet he still has not filed and I know it's pointless for me to even ask why or when he plans to.
Basically I'm really no help here except to say you are NOT alone and the weird behaviors that you are observing that seem like everyone else would raise an eyebrow at are totally valid, and I don't know what gets into our WASs that makes them so blind and susceptible to doing outrageous things. It's frustrating, it leaves us without answers, it leaves us yearning for so much ... but if nothing else I think it's really good that you are seeing the strength and positivity in raising the kids and still thriving in your career.
FYI I protected my H for what I felt was a long time too (2 months). Finally I pushed it and made sure he told at least his parents, and I told mine, and I also told the neighbors simply because I NEEDED to or I was going to die from not having an outlet for what I was going through. Looking back I can't help but wonder if I expedited a process that he may have otherwise started to question more on his own had I not pushed it, but at the same time I couldn't play games anymore and it was getting to the point where I felt like he was waffling because it was convenient for him, as long as I was letting him, even though he was ACTING as if he cared - as opposed to him waffling because he wasn't sure.
Anyway from a social media (SM) perspective, I wouldn't worry about that. There are some other threads on here about that but I have also concluded that I am not even going to touch that until it's really the right time and stuff has resolved. It really is like a whole part of your life is frozen in time and weird that a whole bunch of people you both know may have no idea. You will know when it's the right time for you to let people know and so forth. The only recommendation I would give there is to not be negative about your husband if/when you do share, because the other thing I've learned is that the more they feel shame, the worse the behavior gets. Sometimes we think the opposite, or that if we tell someone else maybe they will help change their mind. In a healthy society and community, I think those types of things would happen, but the reality is that most men do not look upon this type of vulnerability positively, and many "community" members (friends, neighbors, even family) will not attempt to "intervene" or change anyone's mind. It's sad because we are not left with many options then to encourage someone how to deal with such things in a healthier way unless they simply decide to on their own.
H:39 W:30 M:4 T:9
05/2018: H says "ILYBNILWY", BD 07/2018: Discovered A, confronted 09/2018: PA + other details emerge; H moved out 12/2018: I filed 03/2019: Divorce finalized