It will be a great chance for your daughter to put her Japanese into practice. I've been a Tokyoite for 20 years but gradually moving to LOS, the remote work/multi entry option of the DTV is great, so have best of both worlds, at the moment.
no problem, also when you extend at an IO, you can be given an "extension under consideration slip". So you may have to wait and some on return have been told they need to border hop due to some minor discrepancy in paperwork. There are probably countries nearby you want to visit anyway. So visit them and get a new 6mth stamp on return
That's right, it is much easier to border hop without showing cash, filling out forms. When I got my DTV, the Thai officer told me to just border hop, it is so much easier and they were right.
Yes, you need to show it when you extend. Doing a border hop or regular reentry there is no current requirement to do so. You must first border bounce at the 6mth mark not a year though. You can only stay a year without leaving if you extend at an IO.