And I managed once (maybe twice) to wait a whole week before I emailed!!!
So, I think you don't need to wait a couple 'weeks' between emails.
I usually phrased my emails as, "just want to make sure you have everything you need."
Or something along those lines.
They also process applications by order of nomination date from what I was told. I think I saw somewhere you had a September nomination? That could be part of the wait as well (my nomination was June, and I received my placement questionnaire in January, then 3 weeks from submitting that to invite)...