I want to apply for the Golden Visa and want to take out a loan to do so. Is this allowed?

According to the relevant provisions οf immigration law in force, the investor must have full ownership and possession of the property at the time of submitting the permanent resident application, and the existence of a mortgage constitutes an obstacle to this condition. After the issuance of a residency permit, the investor may obtain a loan in Greece or anywhere else, with a mortgage on the acquired property, under the related terms and conditions of each bank. In all cases, the price of the real estate has to be paid via a crossed bank check or through a banking transaction from the Greek bank account of the buyer to the Greek bank account of the seller. So a loan can be taken from your bank, provided that no encumbrances, hypothecs, etc., are on the property. If your bank could provide you a loan with securities beyond the under purchase property, there is no obstacle for the Golden Visa procedure.

In general, banks in Greece do not grant loans for the purchase of real estate to foreigners. If you succeed to get a loan from a foreign bank (difficult, in my view) then yes, it is no problem to have the property paid like this and to obtain the Golden Visa.

It is totally enough. The Greek government does not care about the origin of the money.

Unfortunately, you cannot take a loan from a Greek bank in order to be eligible for the Golden Visa program. However, you can do that from a bank located in your country. i.e., from a domestic bank.