Question One
They wish to see confirmation that you have an understanding of what the role entails and how your past experience and current skills will meet their requirements. I believe they would be looking for specific examples to verify so not just saying my customer service skills are excellent - giving an example of a time you provided excellence.
Question Two
They are checking your fit to their culture and the environment in which you will work. Providing you researched this your answer will have been okay - for example did you reflect that you knew the office was open plan, their policy is open door etc. The question about supervision would be best answered by stating that you like to be treated respectfully, given an opportunity to discuss your performance and criticised in a way that helps you develop, you are able to follow instruction very well though gladly accept responsibility and can be trusted to work within guidelines and use initiative etc. Team mates - something like being supportive and value each others opinions etc.
Question Three
Similar to the first one, any strengths you mention should relate to the job - so for example good keyboard skills, organisational capabilities, strong sense of what matters to clients, ability to manage your own workloads, complete reports and enter data with high degrees of accuracy, able to work under pressure etc - try to put in examples to ensure what you say does not sound like you are trotting out rhetoric.
Question Four
They are looking for you to have a degree of self awareness, to know your own weaknesses, to be willing to develop, that you do not see yourself as being perfect, that you aren't naive enough to supply a huge list or to admit to weaknesses that will have a major impact on this role, that you learn by your mistakes etc.
Question Five
This is to test your understanding of teamwork, to determine if you are a supportive team worker, that you realise how individuals can impact on others in the organisation and that you can get along with a diverse range of people without issues.
Question Six
Clearly this is your chance to really pitch yourself as being the right candidate for the job. They want you to have a hard-work ethic, with all the desirable skills and qualities to be able to perform to the optimum in the role. If you have done your research you will have a good understanding of what they want here. Again if you can supply examples it backs up what you say. So, for example "In my last post I was commended for the number of customers who expressed in writing their satisfaction with the service I provided. I believe the customer must always know that as the representative of the business, I care about how they feel and I do my utmost to ensure their experience with us is of the highest quality. I feel this approach is reflected in thoes satisaction letters"
You can offer the names and addresses of referees at this point who can confirm that your previous employment has been exemplary.
I hope some of this helps you, and wish you the very best of luck for good news soon