1) Do we need to put any deposit with our offer? Can we get it back later no matter if we withdraw or be rejected?
Depends on your contract offer. Your EMD can be due either on the "contract ratification" or "Creditors approval".
You can get your EMD back before the creditor approval. If approved, and you don't have other contigencies, and the HOA reviewing peroid past, then you will not be able to get your EMD back.
2) During the process of waiting for bank approval, can we offer on other property if anything comes up? Are we going to get any penalty if we withdraw our offer?
Yes, you can make offers to other listings. You can safely withdraw your offer anytime before the creditor's approval.
3) It is said "sale as is". How can we prevent the house being damaged by current owner before they move out?
It is sold AS IS at the contract time. Write down, or better, take photos of the condition at the time you submit your offer. If damaged after that, the seller is responsible, though theoretically.
As short sale is a "friendly foreclosure", I seldom see the seller damage the house on purpose
4) Anything else that we need to pay attention to when we draw the contract?
You need a caring agent to deal with all the complications of short sale. Pay special attention to HOA and other possible liens. Insist using your own title company if you have a choice. Request HUD1 days before the settlement date to avoid surprises.
Good luck!