Yes, you can generally search for homes before you acquire financing, but a good rule to follow would be to view homes once you know how much you can afford by at least getting pre-approved by a mortgage lender.

Yes, in California you should put down an earnest money deposit of 1% - 2% of the purchase price. For properties in a slower market you may be able to offer $500 - $1,000 deposit of good faith to secure your interest in that property.

If your deposit was gifted to you by a family member or other approved source you can purchase a home with none of your own money down. You may want to think about getting a government-backed FHA Loan that will require as low as a 3.5% down payment, and look for First Time Home Buyer Programs that will help with down payment assistance.