Hello, I'm new around here (freediver but not spearfisher so have been pretty quiet). Depth is HARD to get around melbourne, in the bay, probably max 10-12m (that I'm aware of such as at pope's eye) unless you want a short swim at slack water and will probably need a boat. Outside the bay is probably a bit more promising but very weather dependant and unless you have friends with boats or can charter one you'll find it difficult to get there.
Pool training: A lot of pools are pretty tolerant as long as you keep out of everyone's way and don't cause any trouble. Most do NOT like static demonstrations although I have seen one exception. I don't think there's anything regular going on (would love to hear about it if there is myself
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Check out the Australian Freediving Association on facebook as well
Edit: I think Monash Uni might run an underwater hockey club that could also help?