Just take out the screen and try to click the connections properly, sometimes it could be just the connection issues. If not it my just be a defective screen. Also, Do you see any lines on the display?

as long as you didnt ripped off the actual button cable it should work. Just do the hard reset on the phone(hold power and home button simultaneously for about 10seconds, until the phone turns off and apple logo appears again) If that doesnot work you probably didnt click the connection too well, try opening the phone and make sure the connection clicks. I sincerely hope you havent ripped off the home button. Let me know how it goes.

Its most likely the lcd problem, either you dropped it or some how put the pressure on phone screen causing LCD to damage. The phone doesnot have to be physically damage on the actual screen, to damage the lcd. Clean your screen and have a good look at the screen, i m sure you will find internal crack over there. Although they are hard to seen.

Follow this link: http://youtu.be/4_UaUfegrM0

Battery replacement doesnot require any backup at all. Infact any hardware replacement doesnot require any back ups, although its safe to do so, just incase you run into some softwares issues after hardware replacement(chances less than 1 in thousands). Sorry to say, you should not have given the password just for changing the battery.

you have specified the model of the phone, but anyways most samsung can be restored the to the factory settings; Turn off the device. Press and hold the following three buttons at the same time: Volume Up key Home key Power key When the phone vibrates, let go of the Power key but continue to press and hold the Volume Up key and the Home key. When the Android System Recovery screen appears, release the Volume Up and Home keys. Press the Volume Down key to highlight 'wipe cache partition.' Press the Power key to select and wipe the cache. With 'reboot system now' highlighted, press the Power key to restart the device. once its restored you can sign in with your google account and retrieve your last backup.

You probably have a third party generic chargers. Make sure to charge with original apple charger that came with your phone.

Doesnot necessarily have to be pierced for the battery to be swollen. infact if your phone is More than 18 months old then most likey the battery gave up. Just change the battery and you will be fine.

yes they are the same.

you will have to restore the phone to the factory settings; Turn off the device. Press and hold the following three buttons at the same time: Volume Up key Home key Power key When the phone vibrates, let go of the Power key but continue to press and hold the Volume Up key and the Home key. When the Android System Recovery screen appears, release the Volume Up and Home keys. Press the Volume Down key to highlight 'wipe cache partition.' Press the Power key to select and wipe the cache. With 'reboot system now' highlighted, press the Power key to restart the device. once its restored you can sign in with your google account and retrieve your last backup.