Keeps rebooting by itself, wont turn off, battery drain fast etc

Hello

I'm having many problems with my iphone 4s, soon after a local mobile shop company replaced the screen (have to mention i kept having to go back to them as it wouldnt charge after and headphone port wouldnt work neither, so i wouldnt be surprised if these problems im having now are due to them...)

anyway right the problems:

it doesnt stay on for long when its not on charge....it will turn off anywhere from 80% to 0%, when it does it will show the usb icon to plug it in and will repeatedly keep showing the icon without pressing any buttons until its completely drained :/ will note that sometimes it will boot back up again strangely...when i plug it in to charge it so that it comes on it will say "this iphone needs its passcode after restarting" and also the battery % when booted up is 30% sometimes so its defiantly turning off way too early...

phone wont turn off, it will just keep rebooting back up

it also now keeps restarting by itself, especially when in an app, its like it cant handle it any more lol.. note that the phone is now jailbroken on ios8 so not sure if its due to that, this wasnt a problem before it was jail broken.

oh and another problem the phone thinks its in docking mode a lot of the time so wont have a sound bar and wont play music or video sound out aloud, quite annoying but i can live with that. this was the first problem ive had with the phone and all the rest gradually happened.

sorry for the essay but thought it was best going into detail... does anyone know the reasons to these problems and ideally how to sort it, and if its worth sorting?

appreciate any help

thanks

Jordan