Divorced

My interpretation would be this: As of Dec 31, they are two unmarried taxpayers.  Treated as such for the entire year as if they were never married during 2024.  The "considered unmarried" requirement that the spouse not live with the other for the last 6 months of the year is therefore not applicable. Even though part of those six months they were legally married, but not for tax purposes. 

I'd say yes, one could be treated as HOH, whoever provided over 50% of the maintenance of the household.  Doesn't have to be the taxpayer claiming the child(ren) since the release of claim to exemption can be used.  Without looking at the code specifically, that's what I think unless someone corrects me!

And for the other half of the equation, please remember that the IRS does not care what the Divorce Decree says about who claims the child, and does not follow that.

I use this tool to determine who the IRS says is entitled to the Dependent

https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent

If the answer from that tool is not who the decree says gets to claim that year, Then use a form 8332  to allow the other parent the dependent for that year.