You must not have been taxed as Portuguese Resident in the previous five years and the pension should be paid abroad.
No, you may simply rent.
No, the transmission of your legacy to your spouse or children would be exempt from Portuguese inheritance taxes.
Yes, circa 50% of the difference would be taxed.
Yes, it would be subject to a progressive tax according to your global income even if it was already subject to foreign withholding taxes by countries with whom Portugal has double taxation agreements.
The Portuguese Tax Administration may take around 6 months but, in case you fulfil the requirements, this Regime is granted to you since the request date.