Should I use garden earthworms in my Worm Farm?

No.

Not unless you have found the right type for worm composting (vermicomposting).
The worms most commonly used for composting are Tiger Worms, Red Wigglers and Indian Blues.
The normal earthworms that you find in garden soil are earthworkers, they burrow and aerate the soil, and will not be happy in a worm bin.