You've taken up a bit of a challenge ... hey?
Wouldn't worry too much about the rivers, presumably the trek route will be chosen to be at least do-able.
For good maps go here:
http://www.thelist.tas.gov.au/listmap/listmapstart.jsp. The maps change scale & detail level as you zoom in & out.
Quick ansa to your questions:
1) How deep are all those rivers (even the little ones)?
... varies between location along rivers and on rainfall. Anywhere between 10cm and several metres at least.
2) How fast do they flow?
... depends on width, rainfall, etc. some are flowing very fast, whitewater Grade 4-6.
3) With using purification tablets are they safe to drink?
... absolutely, I've been drinking untreated water in wild Tassie places for decades, no bad expereiences yet, except some busy places (go upstream there)
4) If we went along them, are their many waterfalls which would block our path?
... depends very much on which river, some waterfalls, but more likely gorges & rapids
Enjoy the prep!
On the run ...

a.