So I have a few fleets with lets just say 2000 plus troops ready to invade a system.  The first round of ground battle it is 600 vs 600.  I have been trying for what seems like 20 turns to take out this system and feel like I am in a stalemate.

1) Is 600 the max out troops of whatever the total pool is that can fight each turn?  It is not very clear and is very confusing.

2)  How is the AI able to field 600 troops every turn when it shows their defenses as zero?

Thanks

As to your first question: yes. There is a limit on how many troops you can deploy on a single turn. You can increase this limit through technology.

As to your second question, what it shows might not be correct. UI is not very informative when it comes to invasion. 

Your opponent can replenish his manpower in two ways: 

1) By using Conscription tactic that converts a single population unit into extra manpower.

2) From ships. Make sure there are no enemy ships coming into system while invasion is in progress.

Watch out for Conscription tactic.

AI is now smarter at defense.

In general, if you feel the system is strong, and enemy can conscript alot (like, 22 pops on planet means 22 rounds of conscription) - just bomb the shit out of it, screw the buildings/pops, otherwise you gonna be stuck forever there.