Answers
Yes, you can. What you cannot do is to transfer the properties to a new golden visa investor without first removing any collaterals registered as encumbrances to the relevant property.
You should consult with the bank from which you will get the loan on this.
In order to get a bank loan to support the establishment of your business, you'll need to show your income or bank deposits or anything proving that you'll be able to pay your loan back to the bank.
You should first consider carefully whether you have the right to set up your own business with the residence permit of the landlord you keep. In theory and by law, you do not have this right with the current legal framework. You can only exercise business activity as a shareholder or chief executive in a company that is already operating. With regard to mortgaging your real estate, you are legally entitled to do this, but Greek banks are positive to lend third-country nationals only if your income is based on euros. You might be considering a short-term or long-term rental of one of your real estate assets in order to set up a euro-based income.