all of the above are great suggestions
another one is putting silica gel in your guitar case
the little packs of silica gel you get when you buy shoes are ideal. just put 3 or 4 of those into your case, and they attract any moisture, rather than the moisture going to the strings.
RE wiping down the strings - you could even try just plain old toilet paper (I hope that's the word that is used in Singapore!). This may work better than fastfret, since it is not a moisture-based product, and you are only wiping 'dry', as it were.
I used to use fast fret, and it's great with new strings, but as soon as one bit of rust appears on the strings, it becomes pretty much useless, and makes the strings very hard to play on. I think the moisture in fastfret must somehow aid the rusting process.
So that's my suggestions - clean strings with toilet paper, and keep some silica gel in your case.
hope that helps.