In form DS156, I stated that you are currently unemployed. If they ask you what you have been doing lately, you can say that you have been studying english by yourself.
In form DS156, I did not fill out when you plan to come to the U.K. If they ask you when you plan to come to the U.K., you can say that within 30 days after you get the visa.
In form DS156, I also stated that both yourself and I will afford your trip to the U.K.
At the interview, if they ask you when you plan to come to the U.K., you can say within six weeks. You can tell them that you need to prepare and spend sometime with your mother and friends. You don't need to tell them that your mother is sick.