xinebessa,
Just to echo what lizplt says, I don't think that the online tests have a major bearing (if any at all) on your results at stage 1. Although NATS don't usually offer feedback various posters on this forum have managed to obtain a small amount of detail regarding where they failed, but I've never read anything by anyone who has been told that they failed due to the online tests.
Lizplt,
I am also still waiting for SHL to email me with the personality test. I got an email on the 13th telling me that I would have to take it and to await a further email from SHL, but nothing since. It seems a bit odd because the email also said, "Once we have received the completed questionnaire a further e-mail will be sent to you regarding the next stage of the process." But I then got an email inviting me to stage 3 almost immediately.
Apparently NATS had some problems with their email system the other week so maybe this is a result of that. I've not got my stage 3 until November 4th so I figure I'll wait until a bit closer to then and if I still haven't had anything a week or so before then I'll contact HR.