The main problem with bin cages for syrians is finding a bin big enough, most will have less floor space then the cage she's used to, I've only used RUB so I'm not sure what else may be big enough but the largest RUB has a floor space of 3834 sq cm while the alaska is 4032 sq cm but someone may know of a bigger more suitable bin.
The best wood for levels or toys is kiln dried pine.
If you need to waterproof wood use Plastikote water based enamel.
Mesh can be anything between 6mm & 13 mm. Smaller mesh makes chewing harder as they can't get their teeth into the gaps.
I would recommend at least one side panel as well as a meshed top for adequate ventilation.
PVA glue is fine for wood toys.
There's a guide to wheels
here flying saucers aren't ideal as a main wheel as they do tend to run with a bit of a twist to the spine.
Sisal string is about the safest for hanging things, you can also use things like pear clips or book rings which are larger so don't trap little feet.
That is a cute adorable pic
She's lovely!