If you just want some leverage on the deposit issue, yes by all means demand some heat. Yes, the lack of heat is probably a breach of the implied covenant of habitability and so is the lack of ventilation. Whether you have a worthwhile case depends on lots of factors, inlcuding the amount of rent you've paid over time and any injury caused.
Re the deposit issue, landlords may hold a deposit of up to 2 months rent for an unfurnished unit and up 3 months rent for a furnished unit. (California Civil Code 1950.5) So if your unit is unfurnished, 2 months rent is the most the landlord can hold. Deposits may be applied by a landlord to make repairs after a tenant moves out; but only for repairs of damage in excess of "ordinary wear and tear." That means the landlord cannot charge the tenant for routiine turnaound costs such as cleaning, repainting etc. or for defects that existed before the tenancy.
In California, the case Green v. Superior Court established that residential tenancies in California contain an implied warranty of habitability. Basically, this means a residential rental must be habitable at the time it is rented and during the tenancy the landlord must repair problems that render it uninhabitable. “Habitability” means the property must be in livable condition. Items under the warranty of habitability include working electrical, plumbing, gas and heating systems, ventilation and compliance with building and safety and health codes, among other items. If the unit you rented lacked heat when you rented it, you probably have a habitability claim. Habitability can also be raised as a defense in an eviction lawsuit. On the other hand, landlords are not responsible for repairing damage caused by a tenant, other residents or their guests. The division of responsibility for repairs between landlord and tenant is usually stated in the rental agreement or lease.
If the heat was working when you rented the unit but stopped working at some point, the answer will depend on whether the heat stopped working through no fault of yours or because of some misuse or damage. Assuming you did not damage the heating system, your landlord is legally obligated to restore heat to your unit. It may be as simple as relighting the furnace pilot.
Regarding the deposit issue, you need to consult your rental agreement. One and a half to 2 months rent is usual but not set by law. If the lease or rental agreement sets the deposit at 2 months rent, the landlord cannot change the agreement without your consent. However, you also need to look at the use or occupancy section of the agreement. Are you the only person listed as an occupant? Is the landlord’s consent needed for others to occupy the unit? If so, she may have the ability to demand additional deposit. Still, 3 months rent for a deposit is somewhat excessive. If your building is rent controlled, the deposit amount maybe limited under the rent control ordinance.