Can I have an interview on a green card in the United States?

No you cannot since you have to be in a valid nonimmigrant status to adjust status.

Not likely unless you will maintain legal status. Goodluck

No. Because you are out--of--status you must leave the USA to your country and apply through the US Consulate. You may be subject to a waiver as a result of your overstay. I suggest you consult with an experienced immigration attorney.

Only if you have maintained lawful status in the US.

Congratulations on winning the DV Lottery! Unfortunately, you must be in lawful status in order to adjust status from within the U.S., with a few exceptions. Chances are you that will have to process the IV through the U.S. Embassy in your home country. However, if you have accumulated more than 6 months of unlawful presence in the U.S. and depart, then you may be subject to either a 3 or 10 year bar from re-entering, unless you have a waiver. The best way to proceed is to consult with an immigration lawyer and discuss these issues. Good Luck!