Looking for work in singapore

I live in Ottawa, Canada and I would like to find a business consultant or civil engineer job in Singapore. Is anyone has an idea how to approach the marketplace. And what wil be the cost of living per month.

To find a job in Singapore, you basically have to be here.
Employers are generally unwilling to pay for travel to interviews and therefore only contact people with local phone numbers.
Getting a work visa is currently very difficult and, sadly, since too many Indians abused the system in the past, people from subcontinent origin are now very often rejected.
Cost of living (especially rent, cars and other luxuries) is high.