As mentioned there is no expat package in SQ. Transport is very cheap for an expensive city like SG. Even taxis. Public transport is peanuts. If you live on the East side relatively close to Changi I doubt you will spend anything near 1000 S$. Rental is super high. If you can take the lifestyle which comes with an HDB flat in a not so central area, you are probably ok. A posh expat neighborhood can be easily a five figure number. Looking for a rental unit? Try propertyguru.sg
Most private schools are a joke. They can't compete academically with public schools. Mate of mine is trying to get his kids out of a well known private school in Katong. Mind you, good public schools are extremely competitive to get in and tuition classes are a part of life here.
I don't have salary numbers. From my understanding variable bonus pay can be a large chunk of your income in SQ. If the company does well 3-6 month bonus pay is not unheard of. How about going to an interview, get a taste of the city and ask for exact numbers?
Good luck!