It's a pretty nice job to have. I've had amazing experiences because of it and of course it's lovely seeing your work on supermarket and bookshop shelves! :)
I don't think Kate's every day high street stuff will make it into the collection unless it's something particularly special like the stuff she wore for engagement photos etc. The more spectacular evening dresses will probably end up in there though along with her wedding dress and future coronation gowns etc. :)
They have a LOT of storage space but the collection is already huge so I think they are pretty fussy about what they keep for posterity so that'll be the most historically significant and special pieces.
I get the impression that the royal children wear genuine royal hand me downs, yes. I suspect they're still in storage at Kensington Palace. Kate has a reputation for thriftiness so I doubt she'd buy something new if she can have a vintage royal original! 
The wedding and coronation clothes go into the collection straight away because they're not likely to be worn again. They also store the ermine trimmed robes, which are so expensive to make that they are used repeatedly. Other things will go in when the owner dies or they're having a sort out and want to move old stuff on.
Most of the collection is stored in boxes on shelves. They're wrapped in special tissue paper etc and its all temperature controlled etc to make sure that nothing deteriorates and moths can't get in. The new department in Hampton Court Palace has a pretty clinical feel to it actually, like a forensics lab!
Hah, no, I've never seen the royal family hanging around while I do my important historian business.
I don't think they mind too much tbh - their residences are massive so we can all co-exist and I think that they like the fact that people are interested in their family history as they are pretty liberal with access. We don't have to sign anything but I think we're so aware that being allowed access to these things is such a huge privilege that we wouldn't want to overstep the mark anyway! :)