Prius 2004/5 queries

Can someone tell me if I have an issue with my 2004/5 prius.
When coasting and recharging the hv the battery gauge shows charge right up to 100%, once it gets to 100% the gauge is green and the engine kicks in and is sat at about 2500/3000 rpm, as soon as I put it into neutral the engine stops running, it's as though a fully charged hv battery causes the engine to kick in!!
My journey to work takes me down two hills every day that cause this to happen
The other query, I'm not sure if it is related. If I have been driving for a whole, either on battery or ICE and come to a halt I notice the engine is running, this time on idle, if I come to a complete stop and wait for about 15 seconds the engine stops running, I've not noticed this before and it happens no matter what the state of charge on the HV

Being new to hybrid I am possibly a bit paranoid, as time goes on I am getting more and more used to the way it drives and behaves.
My final question, I have an iPhone, is there an app that will allow me to get real time info via a Bluetooth obd reader?

Thanks

 

No I don't use B mode would this make a difference to it charging whilst rolling downhill?

I understand what you mean by the "bleeding off of excess charge" it was a thought that passed through my mind

As for the engine running, maybe I should expand on my original explanation.
Before I approach a junction I allow the car to coast, sometimes up to 200 yards if I have the speed, I was under the impression that the engine would switch off once the throttle was released, but mine doesn't always appear to do this, it will coast along with the engine running, once I come to a halt the engine is still running.
It doesn't do it all the time, but it's not caused by specific state of charge either.
I'm still not sure I have explained it well enough, hopefully it does make more sense now

 

Thanks for your help, it puts my mind at rest