I work as a Downey Keller Williams Realtor and a property manager for my dad's business.
Usually in our case, you would need to call and reserve an appointment. Some properties have an on-site manager who is available to show you the rental unit during normal hours.
As for the deposit, are you referrring to a deposit to rent the unit? We rent on a first-come-first-serve basis and do not accept deposits to hold the units. I know that other properties will accept a deposit to hold the rental unit.
Please do contact the appropriate person to begin your apartment search so you are not limited to something you do not really like because you have no time remaining and need in your current residence.
Hope this answer is helpful.