Several methods you can try to figure out this problem. Just as you know, error 4013 occurs where there is a hardware issue inside your iPhone. Method 1: Hard reset your iPhone Method 2: Check out the USB cable/port and the version of iTunes Method 3: Release the storage of your iPhone Method 4: Restart Your Computer, Reset Your iPhone Method 5: Use FORecovery iOS system recovery tool to flash the firmware. Method 6: Try recover by entering the DFU mode
Many problems will probably lead your iPhone stuck in recovery mode. Just hold on your power and home together for about 10 seconds until you see the apple logo on the screen. Then release the power button but still press the home button down. Open your iTunes and go after the caption. Get the details in this tutorial about how to recover stuck iPhone.
Sorry to hear that. Maybe you can try some iPhone Data Recovery toolkit to recover them. You just need to run the program and connect you iPhone. There are three modes inside this toolkit. Maybe you can get further help in this tutorial about how to recover data from broken iPhone 5.
Fret not. Maybe you can try to use some Android Data Extraction, like Forecovery. I have ever met the same experience as you, and successfully deal with it. All you need is to download the program and follow the tips according to the software. Get more details in this tutorial about the methods to recover contracts on Android. Hope this is helpful for you!