why don't the Russians cooperate with them?
Russians won't cooperate with them because then Ukrainians wouldn't have to take food from Russian soldiers and so Russians wouldn't be able to record propaganda videos (just like they tried to do it in Kherson and failed, because people protested against it).
And mayor Stolbovoy was accused of treason already at the beginning of April:
In another article I've read that he told the inhabitants to be loyal to both the Russian military and to the Russian Federation.
Because they don't have to.
They're obliged to do that under the international law:
"Under international humanitarian law, parties to a conflict must allow and facilitate the rapid and unimpeded passage of impartially distributed humanitarian aid to the population in need
. The parties must consent to allow relief operations but may not refuse such consent on arbitrary grounds. They may take steps to control the content and delivery of humanitarian aid, such as to ensure that consignments do not include weapons. However, deliberately impeding relief supplies is prohibited
Apparently Russia claims that there are no children in the Azovstal bunker - here's a video showing that there are both women and children down there:
Dear God... Can't anyone help them?? :((( Russians could show some mercy and human compassion at last and let the women and children evacuate wherever they want... Yes, I realise that's almost impossible to expect that from orcs... :(