1.yes there are free sightsee tours (even incl a soft drink, for free too) route seems to depend on season and wheather [clearly, in Xmas time you cannot escape the Orchard lightings), but I think theyre only in the AFternoon, thus beyond your time.
There is also plenty of (stand up) FREEinternet at many places.
As above tells, its nearly a lounge in itself, and even airside prices are quite reasonable, though not cheap. Note however the difference between the SQ side at T2 and the ''others'' at T1.
There is also a very effective (this is SIN0 METRO=Subway into town, this asks for coins and there is a refundable 1 SI$ deposit on the tokens. Runs so precise on time that you can make the most of your time.