My ipod

so the other day i decided to use my dads iphone5 casing for my ipod touch 5th gent and obviously it wasnt the same size and yea i took it off the next day but my ipod started to turn off randomly when i used it so i decided to never use it again but when i took it off it still did the same thing? and whenever i turn on my ipod back the time & date resets and it goes back to 8AM , 1/1/1970. Also that night i got told to install something that was 'GMail something blablabla' And it said it wasnt trusted so i click cancel but it didnt work so i had to install it.and starting from that whenever i remove my charger from my ipod, my ipod turns off and takes you SO MUCH CLICKING AND CHARGING to turn it back on and the batt last for only 10mins or Less!! And yea also the time & date resets too, is it bc my batt is weak and is in need of a change or was it hacked or something, i really need to know!