Does Minecraft PS4 edition have online and if so how do you access it?

Yes, apparently minecraft has been getting issue complaints though concerning online gameplay. Searched it, been in several site in the past 2 days.

Yes, once you start a new game you will given the option to enable multiplayer.

From the looks of it you have to have person on friends list to do anything online rather than just jumping into a random persons world

It has online.