I think I saw people put them into a big jar and cover with lid in countryside, may as well give a try.

Go to the police office in her hometown and apply for '港澳台通行证'easy to get and for me I got mine by paying 400 years ago, not sure about the price now, no trouble at all.

just try if you could tick or untick that box then you will see.
you should worry about the paying and getting it, would be great if you have friend know how to do this to help you out, it's just trouble since you don't read chinese yet.

you got that right, 全新包关税 / 官翻包关税 first one is fresh product and second one is refurbished.
官方标配 this one here you don't really get to choose, it is ticked with only one option, and it means standard package.

about the postal simply the cheaper one is a different shipping service and EMS is more official by china post, both are safe from my past experience, and EMS is not really faster.

A birth certificate is enough to take the plane.