mobile

I've been using my Nexus 5 for about 5 months now. Recently my phone have been having this "ghost touch" issue. My phone have a cracked screen so maybe that's the problem but I'm not entirely sure. Sometimes the touch screen doesn't work, sometimes it just presses at a spot repeatedly. The second problem is my phone sometimes dies at 80-70% battery if I play a game, use camera, or stream video. When it dies I can't turn it back on as it will die again while rebooting. It can only be turned back on by plugging it to a charger. Third is, when my phone dies or I shut it off, sometimes it will go to the "Android is starting. Optimizing app x of 152.". As I was typing this question, my phone rapidly pressed the recent screen button multiple times. Help is needed as I can't afford a new phone. And I just found out that I have been having difficulty rooting the phone. The bootloader is unlocked even after I've updated to 5.1 but I dont have any root access. I've tried multiple rooting method but failed. The battery problem is really getting under my skin as I love to take pictures but I cant really do that properly with my phone connected to a powerbank.