Verizon iPhone in Europe

I have a 5s running 7.1. I have a Verizon plan.
I am currently in Sweden for about a week and I am planning on using the iPhone in a wifi only capacity. I have turned off cellular voice and data. I connect to wifi and that is working fine. However, I keep getting the "searching" icon in the upper left next to wifi icon. My battery life is a day.

My questions are
1. What is the phone "searching" for? Is it other wifi networks or is it cellular?(even though I have cellular turned off?)

2. Is the short battery life due to the wifi even though the phone is not used most of the day? Or is it because of the "searching" causing a power drain.

3. I thought I turned off all updates and services during my debug of the above. Could I have missed something?

Thanks,
Emp