Oh shoot, I didn't even realise New Game Plus was a thing beyond opening up the global storage box at the start. Guess that explains it. I thought it was odd that A1 (via elevator) seemingly had nothing but a voice recording in it. Ooh, check A5! That had literally nothing the first time around! Also check the "shop" things, as some of them sell clothing and their stock might be different on NG+.
Not sure, but first off, double check you're actually on 0.5.0.1 and not just 0.5 — a couple of the downloads in this thread were mislabeled somehow (one of which has since been updated). From the main menu, hit Updates and it should show patch notes for 0.5.0.1. One of the fixes mentioned was an item not showing up in the wardrobe, so if you're actually on 0.5, that could explain the difference. If that's not it, then I have no idea.