Lost my iPhone and trying to figure out what this Find my iphone message means.

So I lost my iphone a few days ago, at the beach. I honestly thought it was probably gone forever. Here are the steps I took once I realized it was missing:

1. Searched on Find my iPhone and the results were that the phone was offline. Not surprising because the battery was almost dead and there was little cell service at the beach.

2. Enabled "Lost Mode" and set a password to lock the phone in Find my iPhone, with a message to call my home number. I've been checking the last few days and no sign of it.

3. Yesterday I switched my cell service to my old iPhone 4, assuming the phone was gone forever.

So today, I got two email messages at 12:32 (three days since I lost my phone). The first says a sound was played on the phone at 12:32 today. The second message sayss that the phone was put into lost mode at 12:32 today.

What's strange is that the phone is now showing up with the name "S" instead of the name I had originally given it. And when I search in Find my iphone there is a little orange "lock" next to the name of the phone. Find my iPhone is now also saying the phone is offline and that location services has been disabled.

Does this mean that someone found my phone and that they somehow got it unlocked and can see all my data? (I did enable a 4 digit password). Is there a way they could have done this even with the password enabled?? Ugh. Should I click the button to remotely erase the phone??