Not really. Better to go east under i-5 bridge and east of Joe's Crab shack restaurant and park at second parking lot. There is a path to the waterfront. You can see it on satellite view. Down river is Frenchman's bar park.
You are allowed. Not common around that area though. Due to waterfront being added I'm sure it will become more prominent in the area!
Yes although it is rare.
Be very careful in the waters near the waterfront. The water can be very turbulent with undertows.
As far as I know you can .
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