1) Surah Anaam: 21 – The slaughtering must be from a Muslim and the name of God must be mentioned over the slaughter
2) That is okay from non Muslims. Just the meat must be slaughtered correctly by Muslims.
3) If they are idol worshippers they are considered najis, and if they touch the food while it is wet then it becomes najis as well. However if you did not see them touch the food or if they touched it with a spoon then you can consider it pure.
4) If it’s non-meat food yes you can. For meat it must be halal and from a Muslim.