I have broken screen. Can I root my phone only with downloading mode and recovering mode? I want to recover my data from my Samsung S Duos. I have broken screen, so I can't do anything, even unlock (because I have a password to enter the phone). I tried to install CWM and connect with ADB, but USB debugging isn't turn on, so I can't connect with ADB at all. Is there some way to root my phone via recovering mode (with CWM) so I can turn on USB debugging and work with ADB? Maybe there is some easier way to recover my data? I thought e.g. about connecting keyboard to my phone, so I can unlock it and normally connect via USB, but my phone doesn't support OTG :/ any ideas?
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.