You won't get higher salaries than locals as there is a salary scale.
Depending on your level eg assistant/associate or professor. I know that assist lecturer gets about S$10k. Applying for grants are relatively better here. Living standards...depends on your expectations so cant comment except to say that you will be offered the NUS subsidised housing at Kent Ridge Condo (not sure of exact name). It does not have a swimming pool.
An assistant lecturer gets 10K a month??? You mean those guys who don't research or publish, and babysit a class for a few hours a week? Where do I sign up?
That's got to be the highest salary for an assistant lecturer anywhere in the world.