Ive played advanced warfare for the consoles day one of its release and its better than pc in my opinion.
It won't be perfect until they release updates and patch up some errors here and there (for the multiplayer aspect anyway)
but its a work in progress.
as for answering your questions
Lag Compensation: No this problem isn't fixed and its the same in all the previous cods
(unless they invest in dedicated servers in the near future)
Connection Issues: Connection is based off your isp (internet service provider) for example: If two people were to join a public match one person can have amazing connection and experience no lag at all. While the other one hits constant lag spikes and has a chance of disconnecting from the game. Also no, I have not heard of any updates regarding connection issues being fixed.
What is player base size/how active are players: Theres different numbers on each console but more specifically on the pc I would say there is a good amount of active players.
How much stuttering do you notice if at all: It really depends on your pc, I personally never experienced any stuttering when I had the game for the pc.
How much of an issue is hacking: There are always going to be hackers no matter where you are but I wouldn't worry about hackers just yet being that the game is brand new. Usually you would find hackers on the older call of duties such as cod 4, world at war, Modern Warfare 2.