I have broken screen. Can I root my phone only with downloading mode and recovering mode?
I think you should be able to use adb on your phone while in recovery. adb devices should show something along the lines of YOUR_DEVICE   recovery. 

Once you have access to your device in recovery, you can mount the data partition using adb shell busybox mount /data and then you can use adb pull to pull data from the data partition, for example: adb pull /data/ phone_data/ will save the entire contents of your /data partition (which includes apps, wifi settings and app preferences) to phone_data in your current directory. If you want to pull data from your sd card for some reason, simply do adb pull /sdcard/ phone_sdcard/.

Note: I prefer using TWRP (which you can find for your device here), so if any of the above steps don't work you should try using it.