1) yes, Huggies; but you're bound to find that they're quite different to the ones you're used to (we found Aus / US / Sing Huggies to be different - might be to cope with differing climates)
2) king size beds are different sizes, so if you're bringing you're mattress, bring your fitted sheets, too
3) you may find, if you bring lamps etc over, that you can't use them at full power for fear of bulbs going. Plus, if I remember rightly, bulbs in Sing won't fit US style lamps.