What is the ruling on eating in non-Islamic restaurants located in a Muslim country, and is it obligatory to ask about the method of slaughtering meat in them?

Regarding the statue: If you know it to be an idol in their religion, inform the authorities to prevent manifestations of polytheism (shirk). If it is for decoration and they are Muslims, advise them that angels do not enter a house that contains a dog or a picture.

Regarding the meat: If they are Muslims, do not ask, because it is generally assumed that a Muslim would only import permissible (halal) meat. However, if they are idolaters, then if the meat is from within the UAE, eat it; otherwise, do not. If it is imported from the lands of the People of the Book where stunning is predominantly used for slaughter, then it is not permissible to eat it unless you know it was slaughtered.