I don't know if there are different GY-521 boards out there but on the assumption there's no significant variation, this is what I observe from mine:
The MPU-6050 is indeed 3.3V but the GY-521 breakout board includes a voltage regulator so you should just provide 5V (although when I have tried providing 3.3V this has worked too). Neither voltage should damage it.
When the breakout board is powered the red light should be permanently on. It is quite bright.
The breakout board also includes pullup resistors for the I2C lines so you do not need external ones. No level shifting is required between it and an arduino uno.
The connections you describe should be sufficient.
There was no attachment in the last post - can you try again?
It sounds to me like it is faulty (or you are doing something that you haven't mentioned in your post).