Uk general visa questions

Hi,there
I and my sister,both had been educated in UK from 2008 to 2012. Last year,she got a 3-months study offer from Le Cordon Bleu London,but her visa was refused a few months ago and would like to try one more time. I also want to take a trip to UK, just for traveling in Spring.However,we have a few questions to ask. Please help us.

1)I have some questions about on-line apllication form.

I have been issued UK visa in 2008,2009 and 2010.However,I couldn't find any visa information such as date of expiry of 2009,should I just enter my visa information of 2008 and 2010 ? What is the Issuing Authority of my visa？ UKBA or others?

question:Have you made an application to the Home Office to remain in the UK in the last 10 years?
What is the meaning of"remain" in here? To live in UK permanently? If I applied visa for my master degree inside UK,but I don't want to stay in UK permanently. So,my answer is "no", am I correct?

2)My sister's problem is about the reason of refused visa last time. The UKBA said, she had got a degree of hotel managerment in UK, and her offer is about ulinary skills this time, there is no relationship between them. The aim of her study is not clear.
To be honest,I am so comfused now. Why she can not study culinary only because she got a degree of other course.
When she is in Beijing, she worked for a restaurant as chef assistant and find she is really good at this. That is the reason for her purpose of this study. Can she write a personal statement to explain it?

My sister's salary is paid by cash and her bank statement is very mess. To avoid unnecessary risk, can my family sponsor all the fees for her and she doesn't give her bank statement and working information?

We don't want to lie, just want she can achieve her dream.

Please help us!

Thanks a lot