My wife signed a holding deposit agreement for an apartment in Fremont,CA. We are now trying to get our money back since we changed our mind. Is the contract enforceable if only my wife signed the document but both our names appear typed at the bottom of the document? I was not there the day the contract was signed and was unaware of the contract terms until recently.

Second question. Can the landlord/agent claim "lost rental damages" if the place was not vacant to begin with? For example Feb 24th my wife signs the holding deposit agreement with the intention to have us move on March 31st, and at that time we are told that "this is perfect timing since the current tentant is leaving at the end of March".

What does the agreement say? You posted everything but that. Her signature is all that was required.

Have you been approved and notifed to sign the agreement? Have you terminated your intent to rent in writing? It appears they can hold you to any lost rental. If the apartment is rented by March 31, you will have a good case for them to return the deposit. I doubt they will do it voluntarily and you will have to sue in small claims.

with your agreement when was the application accepted
then its 1/30 of the rent from 2/24 to whenever the application was accepted
usually these are the terms for a holding deposit:

HOLDING DEPOSIT

Sometimes, the tenant and the landlord will agree that the tenant will rent the unit, but the tenant cannot move in immediately. In this situation, the landlord may ask the tenant for a holding deposit. A holding deposit is a deposit to hold the rental unit for a stated period of time until the tenant pays the first month's rent and any security deposit. During this period, the landlord agrees not to rent the unit to anyone else. If the tenant changes his or her mind about moving in, the landlord may keep at least some of the holding deposit.

Ask the following questions before you pay a holding deposit:

Will the deposit be applied to the first month's rent? If so, ask the landlord for a deposit receipt stating this. Applying the deposit to the first month's rent is a common practice.
Is any part of the holding deposit refundable if you change your mind about renting? As a general rule, if you change your mind, the landlord can keep some - and perhaps all - of your holding deposit. The amount that the landlord can keep depends on the costs that the landlord has incurred because you changed your mind - for example, additional advertising costs and lost rent.
You may also lose your deposit even if the reason you can't rent is not your fault - for example, if you lose your job and become unable to afford the rental unit.

If you and the landlord agree that all or part of the deposit will be refunded to you in the event that you change your mind or can't move in, make sure that the written receipt clearly states your agreement.

A holding deposit merely guarantees that the landlord will not rent the unit to another person for a stated period of time. The holding deposit doesn't give the tenant the right to move into the rental unit. The tenant must first pay the first month's rent and all other required deposits within the holding period. Otherwise, the landlord can rent the unit to another person and keep all or part of the holding deposit.

Suppose that the landlord rents to somebody else during the period for which you've paid a holding deposit, and you are still willing and able to move in. The landlord should, at a minimum, return the entire holding deposit to you. You may also want to talk with an attorney, legal aid organization, tenant-landlord program, or housing clinic about whether the landlord may be responsible for other costs that you may incur because of the loss of the rental unit.

If you give the landlord a holding deposit when you submit the rental application, but the landlord does not accept you as a tenant, the landlord must return your entire holding deposit to you

I am not evaluating the holding deposit agreement. You need to take that to an attorney in CA for review. This site is not to render legal advice. It will depend on what the agreement says, but it sounds like the landlord took the rental off the market on the basis of the hold, so likely the holding deposit willbe forfeited and that is the end. If you believe that is wrong, you will likely need to pursue that in small claims court local to where the property to be rented is located.