Andrew,
With regards to the personality questionaire, I don't think anyone apart from NATS could tell you what they are looking for (if anything) in it. It's worth remembering though that what the questionnaire isn't is a test - there are no right or wrong answers and there is no right or wrong way of going about it. I'd also bare in mind that the way these things work is a lot more complicated and well thought out than most people realise, trying to trick the system by always "strongly agreeing" is likely to tell them something very different about you than you might think (unless of course you genuinely feel that strongly). I know someone who is an assessor for these type of tests for another company, and it is phenomenol the way they work - after answering about 50 questions they were able to tell me in great detail a lot about myself, and were extremely accurate even when talking about character traits and behaviours that were in no way directly connected to any of the questions... so by trying to trick the system you could end up portraying yourself in a very different light than you realise.
I would also point out that companies who use these kind of tests are often able to ascertain quite accurately how honest you've been in them. If you try and give the answers you think they want to hear rather than the answers that are true for you then I can almost guarantee that they will be able to tell, and dishonesty is one trait that will almost certainly see you not going through to the next stage. My advise; answer the questionnaire honestly and don't try to over think it or analyse what they might be looking for in each question, you'll get your knickers in a twist and will probably end up showing yourself in a worse light than you otherwise would.
There is no checking test at stage 1 (you do one online prior to stage 1 on the SHL website, but rumour has it that this doesn't actually have any bearing on your stage 1 results - apparently you are just being a test dummy for SHL on NATS behalf)