IMHO the Nazis would sort out any remaining Soviets in Leningrad in to several categories:
1. Those scheduled for liquidation such as Jews, party officials, etc.
2. Military POWs as per standards for them by the Germans.
3. Civilians useful for work in the city - grunt slave labor or factory work locally. These would be fed at levels necessary to maintain productivity more for skilled workers, less for those who will be worked to death.
4. Civilians to be transported west for slave labor from domestic servants to factory slave labor.
5. "Useless" mouths who will be left to starve
6. There will be some special cases such as young children considered "Aryan" enough for adoption by German couples or being sent to orphanages in the Reich, and others.
I expect the Germans would tell the neutrals that due to Leningrad being an active war zone, consulates would be closed, and in any case they were accredited to the now "defunct" Soviet government. Any neutrals who remain will find their movements strictly controlled due to "military necessity". As far as neutral food, exactly who could provide it? The USA is the only neutral in 1941 with the potential to prevent mass starvation in Leningrad, and by December they are no longer neutral. I expect the USSR would tell the USA not to send food to Leningrad once the US is an ally, even if there was a mechanism for that, but send that to the Soviet areas still fighting.
To the extent possible, as long as the Germans occupy Leningrad, that anything of value, such as the contents of the Hermitage, and any industrial equipment that could be better utilized back in Germany will be shipped out. Whenever the Soviets do reoccupy Leningrad they will find a destroyed wasteland, with critical infrastructure specifically destroyed (water works, sewage, as well as military targets, the port, and of course cultural icons), the inhabitants will be walking skeletons and few in number.
I can't guess what Finland will do but once they get back what they lost and perhaps some other bits they have no taste for further advances, nor do they have desire or resources to get involved with occupying any Russian town, let alone a part of Leningrad. IMHO the fall of Leningrad improves the German situation, makes the Russian worse. You could likely see the line of demarcation between the Western Allies and the Soviets somewhere in Poland, with concommitant changes in Czechoslovakia etc.