1 and 2 a re intentional, you are not supposed to see a article not assigned, as guest. The TPerror is just for your benefit, so you know it doesn't have a category yet. This might change to allow non-categorized articles, but it means lots of changes that I don't want to add into v1.0 RC1 at this point.
Number 3 I am not sure, but could be related, will need more info about the error.
- About move buttons..I might look at JS based moving of blocks, but this will be for TP 1.1 then, for same reason as above.