I've owned a Civic Hybrid for about 6 years before getting my HS. Here are some of my thoughts based on my experiences with both systems. Keep in mind that the Civic hybrid system doesn't allow for EV mode and only uses the battery to supplement acceleration, kill the engine when in idle, and recharge through coasting or regenerative braking.
1/2/3 - This is normal in my experience. The engine needs to warm up before the computer will allow it to turn off and drive in EV only mode. I'm not sure where you are, but since you posted this in February, I assume that the car's engine is cold when you start it in the morning or after a few hours of not driving. I encourage you to read your owner's manual about EV mode. There are a number of restrictions and the car is smart enough to know when to kill the gas engine and when not to.
4 - I've had this happen in my HS as well. I've found that you can kill the car's power and transfer the call to your handset without dropping the call.
5/6 - This will either be based on your speed or the external temperature.
7 - This is normal and depends on how you drive the car. If you go for extended periods of uphill driving then the battery will get lower than if you engage in "normal" or mixed city/highway driving.
All in all, it seems that your driving experience is pretty standard. If you still have concerns, you should talk to your Lexus dealer... they'll be able to check out your car to make sure that everything is operating as designed.
Take care,
-John