No exchanges should be trusted with the amount you can't afford to loose. You must only store small amount for daily trading. If you want to trade big amount, deposit and exchange it ASAP.
To gain trust, you need to run as long as possible, no big and frequent disputes and it must be run by a trusted person. These don't prevent an exchange to run away, this will only help us to trade there.
Sounds right, but since there's almost no other way of getting BTC than through an exchange you will have to send your money there sooner or later. What if it gets hacked on that day?
What if you're planning to buy something with BTC, can you really afford to lose that money? Sure, you won't be evicted or starve to death, but for most people even a $100 loss still matters.