FM transmitter question

I am hoping someone can give me some assistance on a possible purchase.

I am looking to purchase a Belkin FM Transmitter. The item I am looking to buy is listed below, http://www.bestbuy.com/site/griffin-technology-itrip-auto-lightning-fm-transmitter-for-select-apple-devices/1909017.p?id=1219067155465&skuId=1909017

My questions are:

1. When the battery is charged and plugged in, is the iPod battery draining and then charging as I go or is the iPod staying fully charged while working?

2. Does anyone know if the music/podcast player will stop when I turn of the car, or do I have to stop the player manually?

Thanks in advance.