Glad to offer my perspective. I've been lucky to work with lots of different heads, a couple of whom were perhaps 'misunderstood' by the communities they served but nevertheless worked hard for the children and staff.
Lots of schools your DC's size will have a ft or 0.8 business manager plus a 'front of house' office manager. The financial aspects of school management are rarely, and should not be, managed by a HT, you're quite right. The HT will be focused on curriculum management, teaching and learning as well as assessment, monitoring and accountability. These are all massive undertakings, especially in the light of recent DfE and Ofsted directives. Many HTs are also the DSL (designated safeguarding lead) for their schools, and that can be very time consuming too, and definitely something parents would ever know anything about.
With regards to the course, she did not sanction this herself; her bosses, the governing body, must have felt it was warranted and signed off. Our last but one head made accepting the HT post conditional on a similar arrangement; I'll spend the first year putting new systems in place, and then I want to undertake X CPD, going PT for X time.
Keeping staff in the same year group has lots of advantages. Of course it's fun to try out new year groups from time to time, but LA schools I've worked in have often been advised during annual reviews to keep staff in same year groups; it ensures consistency and people generally get better at doing something if they do it a few times over. I have some favourite year groups, and it is lovely when you start a new academic year feeling like you've totally got it in the bag, and won't have to reinvent the wheel, but can focus on fine-tuning and really drilling down to find ways of making learning come alive for individual pupils.
Finally, the sad loss of the enthusiastic body of volunteers is regrettable. It seems such a no-brainer, right? However, all visitors to schools must be organised and managed by someone. Even if it is overseen by the chair of the PTA, it needs to be overseen to some extent by school staff, checking DBS if applicable, insurance cover for casual visitors who do not necessarily have their own insurance for carrying out work in a school, risk assessment for visitors to the site, unlocking and locking up arrangements, it is endless. As a class teacher, I get so many lovely offers from amazing people and groups offering great things, but the organisation required to get it up and running, if you're going to cross all the t's and for all the i's can be very time consuming.
If your DC are happy, focus on that and get behind your school leadership. You sound like you're open to the possibility of a good outcome.