iPhone 4S Problems. Need help!

First of all,i'm sorry for my bad english.I will try to explain my problems.
I have an Iphone 4s.It's from japan,softbank network.I'm liveing in romania,i have cosmote network and i'm useing a gevey sim to can use te phone here.I have ios 6.1.2 and the phone is jailbraked.
1.First problem is that when i'm tryng to power it off,he is automaticaly power on (so he is autorestart when i'm tryng to shut it down) this problem is the same even he is jailbreaked or not.I restored him but nothing (as new iphone).The only way taht is working is when the phone sis connected to the pc or to the charger,but when i pull the cable out the phone is starting back on (without to use the power button).I notticed that the phone (connected to charger,and off) is charging the baterry (i mean,i connect the cable,power it off,let it connected,and after a while i start the phone and the battery is charged) and i don't know if this is normal.
2.The problem number two is that the battery is drain verry quick.Like 1 percent at maximum 5 minutes.I noticed that in the settings - general - usage - time from last full charge the usage time is almost the same with the stand by time (couple off minutes diference) with the phone in stand by.I tryed to go in settings - privacy - location services - system servicess and turn off all the things from there,i stopped siri,push notificasions and put my accounts (icloud,gmail) to manualy but the problem with the ussage and stand by is the same.I stopped the wifi,edge and 3 g off.Same...and the battery is drainig quickly.What can i do ?((((
I sawed another thing that from time to time (when the phone is locked,i mean in stand by) the phone is autorestarting and i can't see the usage time from lAst charge...i can see just some lines like ---.This happened 5 mins ago,i had 90% to the battery,and after restart i had 93%

 

nobody ?(((

 

Sorry,but for the first point the problem is that i cannot power off the phone.the only way that i can do this thing is when the phone is connected to the charger.If is not connected to the charger and i'm tryng to power it off,the phone is just restarting.

About the warrnety the problem is that ai buyed the phone second hand ( and about the battery i installed a cydia tweak battery detective and he is showing to me that the phone was charge about 160 times

 

Design capacity :1430
Max capacity : 1214
In cydia i have some tweaks but not winterboard or themes.I have activator,sbsettings,ifile,killbackground,open in chrome,stop & snooze,simanager,appcake,vshareremote messages 2,battery detective,attachment saver and some more but unsinfiant.And the thing that i can't power down the phone (without charger or useing it,i mean i'm away from home or tryng to go with a airplane and tryng to power it off,but he is autorestarting,i mean when i'm power it off he is making the same thing like i'm useing the reeboot function from sbsettings) this with or without jailbreak it is the same.I saw something or internet like cleaning the powerdock with a toothbrush or isophropilic alcoohol,i tryed but nothing.

 

?

 

nobody ?

 

and what about the problem with the restart without a reason and the problem that i can`t power off the phone ?

 

Problem resolved ! The problem was from the charging dock.I clean it about 30 minutes with isopropilic alcohol and now everything is fine (i can power the phone off,he don`t restart anymore,the keyboard and lock/unlock sounds are working,stanby/usage normal and the battery life incrased a lot)