I'm not from Singapore but I do know some hard working colleagues who live there.
1. Currently I don't have any offers from Singapore, Is it fine to move there first and try for an opportunity? What kind of Visa should I go for in this case?
I'd rather not risk that. I'm not aware of a VISA that would specifically allow you to squat in Singapore while looking for a job offer.
2. Is there any consultancy from India help us to get a job in Singapore? Please share the genuine consultancy details or links.
There are many. They are all genuine
Whether they intend to help you out is another question.
3. What is the average salary we can get for 8+ exp?
There is no average in any line of work. You are paid by your skill. The more you know, the more you are paid.
4. How about the cost of living for a family?
It is a tad expensive. I've been there and the cost of rent is high. Apartments are leased by the government for X years (99 the last time I checked) if you're looking to buy one. I'm unaware of current monthly rates. The private apartments are more expensive but come equipped with tennis courts and other luxuries. Travelling by cab is expensive. Their train systems are cheap and are on time. Most workers use trains / buses to travel to work. Owing a car is also expensive (at least the last time I asked about it, there was a lottery system to even get one).
