First of all, Air Singapore doesn't exist. It's SQ or Singapore Airlines.
Answer to #4 on your list...
Depending on your phone's data plan and or international use T&Cs, your phone will connect to either StarHub or SingTel - the two major carriers in Singapore. They both offer 3G networks and have pretty good coverage except for the underground MRT system (in some places).
Singapore is a fun city for a few days. If you have some extra time, be sure to check out the Botanical Gardens, Singapore Night Safari, go to Raffles and have -ONE- Singapore Sling, go eat some food at the outdoor food stalls, and go up on the Marina Bay Sands sky deck for an amazing view. If you're feeling like some cultural flavor, head to Little India or China Town. If you're staying inside the city, check out Chijmes for some really fun bars (especially the Spanish Tapas bar with outrageous Sangria). Clarke Quay also has some good eats and some weird bars/clubs.
Things you can skip: Singapore Flyer (think London Eye, but slower), Hop On Hop Off buses, any sort of bus tour, Resorts World Sentosa.
Have a great time in Singapore. Stay away from the durians, leave your gum at home, and don't bring in any cigarettes. Lastly and most importantly, don't forget to pick up some duty free when you land. You can buy 6 cans of beer and one bottle of hard spirits as a tourist. Alcohol is insanely expensive, so if you drink at all, it might be wise to get something for your room to save you a small fortune on bar tabs.
Have fun!