Helen... I assume this is your first Alzheimer's care job. All that you described is typical and normal for this disease. The Alzheimer's has taken away her short term memory. Her ability to think and reason as we do. Her ability to perceive her surroundings as we do.
She wants to leave because everything around her is confusing. She doesn't know where she is or why she is there. Going "home" is nothing more than her desire to leave the fog in her head behind and go back to a time (not a place but a time) when she was not confused. What you need to do is learn all you can about the disease.
Rule number one... do NOT argue with her. If she tells you the sky is red and the grass is purple just smile and nod. You do not have to correct her. If she wants to go out then go for a walk with her. If she doesn't want to sit in the kitchen and eat then leave finger sandwiches beside her chair in the den. She will respond better to routine along with peace and quiet. The same schedule every day is helpful. A loud TV can be very confusing since she can not follow what it is saying. If there is a horrible new story on, then she may think it is affecting her. This can be scary which can lead to agitation. Shadows can be misunderstood as well. Be sure the house is well lit and curtains used to prevent the long shadows of sunset.
For many, morning is their best time. They are rested and relaxed if they have had a good night's sleep. The day is new. As the day goes on they become exhausted and frustrated. When they don't know what you are asking or what you are doing... NO is the only answer they know to give you. She may very well have difficulty understanding what you are saying to her. To many with dementia our words sound like a foreign language. Just words with little or no meaning. She may also have difficulty expressing her emotions. Words do not come easily. This is frustrating to her as well.
When all the frustrations from 100 different angles converge on her she only knows how to do one of two things.... our basic instinct.... fight of flight. She will either fight you (hit you) or try to flee (run away and go home). What you need to do is make her life as routine, peaceful, and calm as it can be. This will help prevent that fight of flight moment. If it does come then you need to learn to distract her. Give her something she enjoys. Hand her a soft blanket to hold. Give her a pretty picture or family photo that she might recognize. Give her a big bowl of ice cream or a piece of candy.
You will not be able to force her to eat. Asking her or begging her to eat is only going to further confuse her. Many times it is in the way you present the food. She has to know that it is food. As amazing as that sounds she may not recognize what she sees as food. Find out when and where she ate before dementia. If she ate at the kitchen table then that is where she needs to eat. Make sure the plate is a different color from the food. A bright colored plate that contrast with the food is best. Give her foods she might recognize. Give her one food at a time and a fork or spoon. Too much will overwhelm her. Foods that she can pick up might help. Sometimes they do not want to be fed so give them something they can feed themselves. Sometimes you can use smell to help as well. We associate food smells with eating. If that doesn't work then leave finger foods where she will know to look for them like the kitchen cabinet or the table beside her usual chair. If necessary help her but do it in a way that is not threatening. Put the food on the fork, put it in her hand, and see if she will put it in her mouth. You can always supplement what she doesn't want to eat with a supplement such as Ensure or Boost. If they are not wild about the liquid, throw in some ice cream and make a milk shake out of it
Be creative, non confrontational, and patient.
Call the local Alzheimer's Association. They have training classes for caregivers of patients with dementia. They also have literature, books, and other information
If you have any specific questions please feel free to ask
And good luck with your charge!