Lots to unpack here.
The strata manger is correct in that at the agm a budget for the admin and capital works fund need to be presented. The owners then vote on the levies based on the budgets.
But no one said the budgets have to be reasonable.
A carefully prepared budget will be a good guide to the costs of running the building. Since you have previous years expenditures, it’s easy to make an estimate.
I say the aadmin costs will be what they are. You can hope and scrimp as much as you like but at then end of the day, the costs are generally fixed. If mid year you run low on admin fund money, they only action is to raise a special levy.
As for the strata manger charging to do research. Look at their contract. Usually they have charges for retrieving documents. Remember the strata manager has to make money, so tasks outside the norm are usually chargeable, especially if they have to go into the archives.
I also question why you are having so many informal meetings. Get them convened as committee meetings or general meetings. Then you have a formal record of the agenda and a record of the decisions . A meeting to decide a meeting is just a waste of everyone’s time.
If you do seek the appointment of a compulsory strata manager, these informal conversations will not carry much weight.
Show that you requested formal meetings , with the agenda items , that were rejected by the committee/ owners
I would be working with the strata manager. It seems that some owners are overruling the strata manager and breaching the act. I sense that your strata manger may actually know what they are doing, yet subsumed by some owners.
Also any owner can put a motion to a general meeting. It does not require the approval of anyone for an item to be placed on the agenda.