If i do remove it, does my existing sketches with parallel lcd work?
Yes. FMs library will run your existing sketches.
Does this i2c backpack require all 16 pins attached on the lcd-backpack or can i use 4-bit mode lcd with the backpack?
You don't have to connect the four adapter pins that go to the lower four LCD data pins but all you will save by not attaching them is a tiny bit of solder.
You must use the 4-bit mode because the I2C adapter does not drive the lower four LCD data pins. The library takes care of this for you when you invoke the proper constructor.
Don