Panama has a territorial tax system, which means that you are not taxed on any income you generate overseas (such as your pension), even if you spend the funds in Panama. This applies to anyone, Panamanians, foreign tourists or residents.
If you are not generating income in Panama you do not have to file a tax return.
If you are working in Panama or generating any passive income here (such as rental income) then you will have to file tax returns in Panama (unless your employer is deducting the taxes from your salary) and pay taxes. The personal tax rates is a combined scale. Basically you pay nothing on the first $11,000 net and then you pay 15% from $11,001 up to $50,000 net income and 25% on any portion above that.
Most of the tax deductions you are used to will also be applicable in Panama. It is wise to have a Panamanian accountant assist you with your tax return.