I currently have in my shop, a 20 amp outlet directly below my panel which is approximately halfway along one of the walls. Instead of having the GFCI outlet at the end, I would like to replace the existing outlet with a 20 amp GFCI outlet and add regular outlets to the left and to the right of it along that wall. Can I pigtail the black and white wires? Will the outlets be protected?
Yes, look carefully at a GFI (or equivalently GFCI) outlet:
You can see the terminals at the top are labeled Line which means, upstream power. The pair of terminals at the bottom are labeled Load, which means this is where to connect outlets downstream which are protected by this GFI.
Be careful not to bridge the line terminals to the load terminals! A pigtail should only connect to the load terminals.