Q. A rental agent showed me an apartment that I didn't like. Afterward I saw a nicer one in the same building, advertised online by the management company, that I can rent directly for no fee. Do I still have to pay the broker?
This depends on the brokerage fee agreement that you probably signed before seeing the apartment with your agent. It is not uncommon for such an agreement to have a provision that requires that you pay the broker a commission if “you rent an apartment in a building to which your agent has directed you, whether or not you saw the specific apartment with your agent” during a specified time frame.
If your agent brought you to see a listing in a building, and you then learned that the management company had other listings there and you contacted them directly to avoid paying your broker a fee, that would be inappropriate and could give rise to a claim of breach of contract if you signed a fee agreement.
If you did not sign one, then under these circumstances you would not be legally required to pay the broker. Ethically, however, it's a slippery slope, particularly if you contacted the management company afterward in order to avoid paying a fee to the broker who introduced you to the building in the first place.
Q. My landlord wants to deduct the cost of removing the California Closets I installed from my security deposit. Is that legal? Does he have to prove that he actually removed them?
Yes. A typical lease requires that you elicit your landlord’s permission before making any alterations or improvements to the apartment. If you installed California closets without obtaining permission to alter the apartment and to leave those changes in place after your lease terminates, and your landlord now wants them removed, it is your obligation to restore the apartment to its condition at the time that you took possession of it.
Your landlord may use your security deposit as reimbursement for the reasonable cost of repairs beyond normal wear and tear, including the removal of unauthorized improvements that you made. If your landlord takes any deduction from your security deposit, they must provide you with an itemized list of the cost of each repair, along with any funds remaining, within a reasonable period of time after the termination of your lease. You may insist that they provide receipts to prove that the repairs were actually performed, but unfortunately you do not have a right to personally inspect the apartment to see for yourself.