英國居留考試!!!!!

For 入籍試 (Living in the UK Exam), you can refers to:

http://www.ukchinese.com/uk
http://www.ukchinesetimes.com
http://www.lifeintheuktest.gov.uk/

They have sample questions on the website.

Also, there are companies who have published books for the exam, e.g. http://www.uktestonline.co.uk/

You can apply with the homeoffice re: your mum's visit/stay in UK. For reference:

http://www.ind.homeoffice.gov.uk/applying/generalcaseworking/familyvisitors

Generally, 6 months does not require visa but if your mum intends to stay over 6 months, you may need to have interview with the home office. As your husband is UK Citizen, it should be fine.