Working for Singapore company while living in Germany

A FRV usually includes the right to work.

However, the formal setup of what you have in mind will be quite complicated:

• Your Singapore income will be taxable in Germany. (Check with your employer and local authorities how they deal with this in Singapore!)
• Since you have no employer in Germany (who takes care of tax and social security deductions - and pays half of the latter), you will be classified as freelancer or need to register a business and you have to pay the full dues from your own pocket.
• If you are less than fluent in (buerocratic) German, you will have to engage professional help for the associated formalities (registration, accountancy, tax declarations, etc.) and pay the fees for this.
  
  

These things are far more complicated here than in Singapore, and the costs make such a proposal unattractive in most cases. In addition, to set things up will take several months - the residence title and work permit alone can take three months or longer, during which time you cannot yet work.