This is a tough situation. It sounds like your mother has gotten pretty sick, and her appetite is poor. Sometimes, when people get an infection (like a UTI), they can
get weak and confused. Her poor swallowing and lack of appetite may be related to the infection, and this problem can sometimes improve once the infection is treated. However, sometimes the swallowing problem is related more to an advancing dementia (forgetting how to swallow) or a stroke (losing the ability to swallow well). If this has happened in your mother's case, it is not something you can fix or change. What I would recommend:
1) See if she improves after the infection gets treated. Most people who lose their ability to swallow (from strokes or dementia) will not improve once the infection has cleared. Keep in mind that some people with swallowing problems cannot handle liquids. They will cough or choke when being fed. This can be dangerous, as they will often swallow things into their lungs, which can lead to a pnuemonia. If this has not been an issue, then I would see how it goes. I would also concentrate more on liquids then solids at this point, as dehydration is the biggest risk. If she doesn't drink well, dehydration can also cause lack of appetite and inability to eat, as it can make people confused. I would feed her slowly and gently, encouraging her to sip liquids throughout the day.
2) If the UTI has been treated now for a couple days, and you see no improvement in swallowing, I would have her swallowing professionally evaluated (like a speech language pathologist). You can get her referred to one by her health care provider. Speech pathologists evaluate swallowing ability and make recommendations about special foods or liquids that can help the person eat better.
Lastly, to address your question about how "long she can last in this stage". If your mother really has lost the ability to swallow, some people can live a couple of weeks or months if just drinking fluids. If she still eats some solid food, she could last months. If she cannot eat any food at all, she may live only for a few days to about one week.