Yes, your allowance is different for each different country you enter, according to each country's laws. As long as you don't bring back undeclared, you won't be breaking the law.
You have to adhere to that country's regulation for duty-free imports. Say, if country X allows 2 bottles of wine, you can buy your 2 bottles here in DFS or 1 each at DFS and country X airport.
For TS, please take note that not all countries like SIN where you can buy duty free on arrival. Most airports only allow duty free purchase on departure / transit.
Sure. The red wine is governed by the duty-free allowance at Taipei. The Martell falls under Singapore duty-free regulation, and your trip is taking over 48h.
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