Re: Polishing exterior & cleaning of interior
don't worry, this is pretty much normal lol!
what happened is that the bird poo, which is highly acidic, has etched into your clear coat. An abrasive polish/compound such as Optimum Compound on a orbital or rotary should be able to "remove" the etching (though technically, you're really leveling the clear coat around the etching to remove the mark).
In my opinion, there's not much you can do by hand to get rid of the mark as it is... only an abrasive compound/polish with a machine will do it... if you wish, you could try scratchX by hand with a foam applicator, but i've done that with very little success.
with regards to your second question, prevention is better than cure unfortunately. The problem is that Singapore is so hot, that your car heats up pretty fast. The heat tends to bake the bird poo on your paint thus etching can be achieved in a matter of minutes. If you see bird poo on your car, you should remove it immediately if possible. The bird poo etch is worse than "water marks" in my subjective opinion. As such, I always carry a microfibre cloth in my car with some quick detailer with good cleaning properties e.g. zaino Z6, Finish Kare 425, QD strength ONR etc. But you can use anything that you find handy if you wish.... e.g. a bottle of tap water (though this might make things messy by leaving water marks or streaks etc.). Better still, don't park under trees or bird-poo prone areas.
having a sealant or wax on your car should provide the protection some protection against bird poo though i've heard that wax is better than sealant for this case. A very durable wax like collinite 845 should give you very good protection against bird poo, as well as acceptable shine/looks (depending on your standards of course). That said, no wax/sealant can withstand the damaging effects of bird poo if it was left on your paint for some time.
hope this helps.