It's a treacherous area for children, so I would have that top of your consideration in terms of spots.
The beach itself has a lot of rips and sweeping waves. One minute you're in knee deep, the next over your waist - depending on the swell and stage of the tide. I stick to patrolled areas for the kids swimming.
Would be mainly small snaps on the main beach, and the odd kahawai - judging from kontiki fishing I've been part of in recent summers.
There is a small wharf/jetty to the left of Anzac Bay which is a reasonable spot to fish off at higher tides. Safe and there are kahawai under the overhanging trees to the left. Nice swimming in the bay for kids.
The point jutting out to the harbour entrance around from Anzac Bay has vicious currents on the outgoing which I wouldn't let small children anywhere near. If they go in on an outgoing, they're gone. Seriously.
Maybe on an incoming tide you could fish here, casting towards the Bowentown estuary you might pick up a kahawai or snapper.
I've hooked kingies there on stickbaits, but landing them was tricky.
It'd be worth going to look at Kauri Pt wharf, well up the harbour, where there are lots of kingies and mackerel etc right under the wharf, and snapper if you cast out to the channel edge. It gets pretty crowded, but interesting.
Walking out to the harbour edges at low tide would give opportunities for casting lures for kahawai etc. There's a community of fly fishers and lure fishers who do that for the kingies in the harbour. Again, have safety in mind re the incoming tides, making sure you don't get cut off on the other side of a deeper inlet.
Not sure about freedom camping - pretty sure it's strictly regulated with very few designated areas. The Bowentown campground is right there, so that'd be your best bet.