Firstly, I assume you are playing on one of the official servers?
A) You leave freeport. At the NPC town there is a pier, at the end of the pier is a ship vendor, if you bring him the materials he can make you a raft or ramshackle sloop so you can sail out of freeport. The zones you can not build in are freeports and golden age ruins grids.
B) There are four freeports. The freeport will always have 4 identical islands at the North, East, South and West positions (rotated but identical). Golden age ruins (the other zones you can not build in) are the 8 grids surrounding the centre grid (Centre Maw, where the Kraken is summoned).
C) Rent does not exist in Atlas unless someone chooses to charge it, but there is no mechanic to enforce this. What they possibly incorrectly referred to I imagine is Island Taxes. On PvE the owner of an island you gather resources on will get 20% on top of what you gather, so you lose nothing (you harvest 10 wood, they get 2, you get 10). On PvP the tax is removed from what you gather up to a max of 30% set by the island owner (you harvest 10 wood, they get 3, you get 7).
Safety on atlas depends entirely on what server you play on and other variables.
D) Someone places their flag on an unclaimed island and after their flag fully raises (1 hour?) they own that island. You can contest this process by being inside their flags radius. They have to keep gold in the flag to pay 12 hourly upkeep. The flag can also pay and feed NPC crew on the island with some settings for this available to the island owner. If there is not enough gold in the flag when the upkeep needs paying then the claim will be lost. On PvP enemy companies can attempt to steal your claim during combat time (9 hours each day, set by the island owner). To contest you place your flag inside the island owners flag radius and remove all of their players and NPCs from inside their flag radius, then their flag will declaim before yours starts to claim.