"Why some ships cant be put on sentry?"
Could you be more specific? That question can not be answered with any certainty. It might be that your ships are in a system with enemy ships in it. If so, you can not place them on sentry in sequential turn mode games because sentry is cleared when an enemy ship enters the system.
"When a green/red planet is not the first (a moon), then you dont have a visible clue. Do you know how to circument the problem?"
Click on the sector and look at the moon.
"Is population really that important? You only get an handful of percent bonus when you add pop to a planet. Seems much effort for a poor bonus. "
Yes, population is important. A 30% bonus to construction and production on _every_ planet in the empire is a huge bonus.
"How do you filter/handle your ships so that you can play fast turns, but without forgetting important fleets?"
Use the next fleet button to cycle through fleets. Fleet all ships that can be fleeted.