My macbook pro trackpad and keyboard stop working overheats when secondary display is attached

Hi, My macbook pro has three issues.

1. If a secondary display is attached via the thunderbolt adapter, it heats up like crazy and then the trackpad and keyboard become unresponsive.

2. When any usb device is connected, the keyboard and trackpad freeze up for over 10 seconds.

3. When plugged in and the lid is closed, I then plug out the power supply and put it in my bag only to find out that it heats up and battery drains, and when I open the lid back up it's unresponsive, forcing me to force shutdown and restart (losing my unsaved work).

I took it to the Apple authorized dealers where I live and they did some preliminary diagnostics and found no errors. Any ideas what the problem could be?