Quite complicated problem you got here.
Never use CWM to flash kernel. Good luck. 

Try check bootanimation in /system/media
If there got no bootanimation.zip, extract bootanimation from rom.zip into your xpro and set permission for it

I have this issue also before. Always with the powerbank or the phone will die.

Buy new battery, issue still occurs, flash stock ROM, still same.
So, I read this one post on xda and calibrate my battery gauge.
Voila! No more issue. Using my phone the whole day now without any powerbank.

Heavy usage around 7+- hours, moderate usage can last around 18 hours. Minimal usage around 1 and half day.

In the end, I don't really know if my old battery is the real issue or not.  Never bother to try to calibrate since I put in on the box already. Lol

Sorry. I don't bookmark the page. Darn it.

But this is what I did if I recalled correctly.

1. Charge your phone to 100% and fully drain it. Just use it normally to drain it to 0%. To make sure it's fully drained, try to boot the phone. Only red led will light up if the battery is 0%.
2. Take out the battery from phone for at least 30 minutes.
3. Put it back and charge the battery to full non stop (do not turn it on) .
4. Pull out the charger from the phone and plug in back for 5 minutes at least to make sure the battery is fully charged.
5. Boot into recovery, wipe battery stats (I'm not sure this steps is necessary or not)
6. Reboot the phone and when the when you see the Sony logo, pull out the battery. Then the charger.
7. Put your battery back and use it like usual.

I might missing some steps there.