What's the reasonable time that we should give to the seller to find the new home? Whatever you choose, but make sure you write it clearly in the contract.
Also can the seller back out the deal if he could not find a new home after we have have paid the deposit already? Yes, if within the contract terms. Your deposit will be returned.
Escrow should be opened as soon as your offer is accepted and all parties have signed the contract. Since you state you've already paid the ernest money deposit, this tells me escrow is open.
If your contract doesn't state a 'time limit' on the seller finding a new home, you might want to see about doing an addendum to the contract setting a time limit. Otherwise, they could take as much time as they want and/or need.
Yes, the seller can back out of the deal if they don't find a new home. This is why they have the contingency. You should get your ernest money deposit back if this happens - this should be stated in the contract you signed.
These are all good questions and who ever is representing you and got you into escrow should be answering these and making sure you are satisfied.