I am very sorry to hear that your mum's cancer has got worse. It must be very hard for you all and especially as you were getting used to the thought that she had got rid of it. It is good though that they are able to offer her a new treatment. Although it does not work for everyone, you must hope that it will work for your mum. 1 out of 5 is not so bad, same as 20 people out of a 100 and you should think that your mum is one of those 20. If things changes along the way, you may have to change your hopes as well. Who knows - the treatment may even go so well that you can increase your hopes further down the line.
Unfortunately, we are not able to give you any advice on how she can live longer. You must remember that medical expertise in the UK is very good and we are confident that she is getting the best treatment and advice that is possible. Doctors in the UK are very specialised and up to date on all new treatments that are being developed around the world within their area. Her doctors will make sure that she gets the best treatment available now or if anything new comes up in the future.
Then - what can you do to help your mum? I am sure you are already doing a lot for your mum and just the fact that you are writing to us asking for advice, proves that you care a lot for her and she must be very proud of you. Many people get very tired when they are having treatment for cancer so maybe you could help out with some of the household chores. First of all, doing your regular duties without your mum having to nag you and maybe you could see what extra tasks you could help with around the house. (Cooking, cleaning, dusting, shopping etc.) It would also be good for your mum to know that you are keeping up at school and doing your homework.
These are all practical things and you can also help her in other ways, like keeping a friendly tone and try not to rebel too much and have silly arguments about stuff that are really not that important in life. The best thing to do would be to ask your mum about how you can best help her.
You must not feel that you should spend all your time at home with your mum, supporting her and helping out in the house. It is probably also very important for your mum that you are having as 'normal' a life as possible and are also spending time with your friends. In times when things are difficult you need breaks from it all so you must not feel guilty about being with your friends and even having fun with them.
Your last question is "why her?" This is a very common question, but in most cases we really do not have an answer. We have lots of statistics and know something about how certain factors can increase our chances of getting cancer, but in most cases we don't know why that particular person got cancer. We do know though, that about 1 out of 3 will get cancer sometimes in their lives so it is a very common disease. Of course, cancer is more common as we get older, which is why most of your friends' parents do not have cancer and it is easy to think 'why did it have to happen to your mum?' The most important thing is that usually no-one can be blamed - we just have to accept that what we think only happens to others sometimes actually happens to us no matter how hard and unfair it may seem.
Good luck - I hope that the treatment will be successful and that things will work out for you all.