Both statements from Azerbaijani President Aliyev and provisions outlined in the 2020 Nagorno-Karabakh Ceasefire agreement answer your main question and your questions in the second paragraph.
President Aliyev's official Statements:
Has the government of Azerbaijan made any declarations concerning what it intends to do with the ethnically Armenian population of the Nagorno-Karabakh region in the event that Azerbaijan regains control of it?
From the English sources I have found, Azerbaijan has made some vague official statements about what it intends to do with the ethnically Armenian population of the Nagorno-Karabakh region. The main story originally reported by Russia's RIA news agency states the following:
Azeri President Ilham Aliyev has said he would not rule out what he termed “cultural autonomy” for ethnic Armenians in the mountain enclave of Nagorno-Karabakh, Russia’s RIA news agency reported.
Aliyev on Thursday also said he was not against introducing observers and peacekeepers to the region, but that Baku would present its own conditions.
Similar text has been reported on as well by Reuters, Al Jazeera, and news.ru. However, President Aliyev has defined one parameter of Cultural Autonomy, that it will not include outright independence as the APA reports:
"We offered them many times different ways, but they rejected. We offered them autonomy inside Azerbaijan. We offered them cultural autonomy, we said that there are good examples in the world, in Europe, in Scandinavia this Aland Islands, in Italy this South Tyrol district, in many other. But they rejected everything. They demanded independence only. And they wanted us to recognize this independence. By doing that they actually knowing that we will never do it, they were doing everything to freeze the conflict. So, I don’t know, we need to first to end this hot stage of the conflict, come back to negotiation table. Armenia should make these commitments which I already said. And then we can talk about what will be happening in the future. I cannot say anything about that now," the head of the state noted.
Autochthonous Armenians and a POW exchange
That is, has it indicated that it will allow the autochthonous Armenians to stay, or that it intends to expel them?
I could not find specific statements put out by Azerbaijani officials concerning the fate of autochthonous Armenians inside Nagorno-Karabakh specifically. Absent these statements, I will default to what the signed Nagorno-Karabakh ceasefire agreement details. In particular, provision 7 covers internally displaced persons, which include autochthonous Armenians:
- Internally displaced persons and refugees shall return to Nagorno-Karabakh and adjacent areas under the control of the Office of the UN High Commissioner for Refugees.
Has it announced any plans to charge current or former members of the Republic of Artsakh's civilian administration and armed forces with any crimes, or conversely that a general amnesty will be offered?
There is no comment one way or the other about any amnesty toward nor charges against any member of the current or former Government of Artsakh or subsidiary authorities. Furthermore, there is nothing in the agreement about said officials either. There is however a mention of a POW exchange in provision 8 of the agreement, which would count as "amnesty" for the portion of the armed forces that served under the Republic of Artsakh:
- The exchange of prisoners of war, hostages and other detainees as well as the remains of the fatalities shall be carried out.