Is Arduino UNO going bad?

has my arduino gone bad, or have I done something wrong in the code ?

These prints where taken without doing any physical changes to the arduino, if you notice pin 10 state is changing between LOW and HIGH without any physical changes or connections !
while the prints where taken pin 10 was not connected to anything.

What could it be ?

An unconnected input is "floating" and its state will be random, just as you observed. To prevent floating we connect the input to a known state. That is where pullup or pulldown resistors come in.

See the digital pin tjutorial.

No surprise there if you do not have a pullup or pulldown resistor connected to the pin to keep it in a known state. It is picking up electrical signals from the environment

Try pinMode(10, INPUT_PULLUP); to turn on the Arduino's built in pullup resistor

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