As a Golden Visa holder, you can keep your tax residence outside Portugal, as long as you don’t spend more than 183 days in Portugal. If such occurs, you will become a tax resident in Portugal. As for the income generated and received in Portugal, should there be any, this will be subject to taxation in Portugal.
Yes, you can. As long as you don't stay in Portugal for more than 183 day per year, you are not considered as being a tax resident in Portugal.
You can keep your tax residence outside Portugal as a Golden Visa holder.