I have a question on mini-wonders and the things they produce (never tried this before). If I switch to Fascism, I will be able to build "Military Research Center" . If, after building it, I switch to another government, will it still produce "Early supertank" and will I be able to upgrade them?
If an autoproducing SW at the end of the turninterval of the autoproduction has not access to the resource, that was needed for the construction of that building (not the resource that is needed for the unit that is autoproduced !) or is not in the demanded government that is needed for the construction, the unit will not be autoproduced in the turn at the end of the autoproduction interval.
Per example, if the city that holds the SW 'Cruiser Project" at the end of the 8-turn-interval is not in access to the resource coal, the base unit 'Hull (Capitalship)' that can be upgraded to an armored cruiser and later a battlecruiser, will not be autoproduced in that turn. If the city that holds that SW only looses its harbor, that is also a perequisite for that SW, this doesn´t effect the autoproduction of that unit, but the base unit needs a unit with the function to upgrade naval units for upgrading the autoproduced unit (that´s why I mostly gave those autoproducing SWs the barracks- or harbor function for upgrading those types of units.
In your example the SW 'Military Research Center' needs the government Fascism that it can be constructed. If you are not in government Fascism at the end of the turninterval for autoproducing the 'Early Supertank', the unit will not be autoproduced in that turn.
Units that were autoproduced follow the normal rules of upgrading. If your civ has one (or more) autoproduced 'Early Supertanks' they can be upgraded, if the city holds a building that allows the upgrading of that unit (p.e. with the 'barracks-function' for upgrading land-units) and the city is in access to resources that are needed for the normal upgrading of the unit (not the resource that was needed for constructing the SW !).
So per example for Russia the autoproduced 'Early Supertank' can be upgraded to an IS-2 and later a KV-5 tank, even when the civ is no longer in government Fascism, when those tanks will become available. If your civ doesn´t have such an autoproduced unit, of course there is nothing that can be upgraded, even if your civ has researched the needed tech for such an upgrade, as nearly all those autoproduced units are set, that they cannot be produced directly. This is also noted in the civilopedia.