Can a landlord evict a paying tenant?

My mom pays rent for a Queens, NY every month on time. The landlord did not give her a lease but she was told that the rent was $1400 and she paid just that. The only thing he has fixed was the water leakage in the bathroom when she first moved in. He refuses to fix the leaks in the house because it snows a lot where I live and he does not provide a doorbell. The bell all of a sudden stopped working after she moved in. He claims that the bell with and without the intercom is get this... $6000! No bell is worth that much. The fridge leaks and water seeps in through the window when it rains and snows. He has security and his rent payments every month and my mom got fed up and asked him to fix the defects in the apartment and he told her that he was gonna get a lawyer to send out a letter to her for her to leave because he doesn't want to fix anything. He does not provide heat meaning the heater doesn't get hot and the apartment is freezing cold in the winter. He does not pay water, gas, or garbage pick up. On top of that he said he wanted to increase the rent by $200. there anything she can do? Does he have the right to kick her out even though she pays rent on time every month?