First of all, 20" wheels are not more expensive to run than whatever else size your dad buys (unless he plans to buy a significantly smaller TIRE). My guess is that your dad is going to replace the wheels with a smaller diameter wheel, and at the same time buying a smaller diameter tire (not just smaller rim size). Should he drive to a tire shop and pick out new wheels, the shop will likely pick a tire that is similar to the stock diameter but with a smaller hole unless your dad specifies otherwise. Then for your dad, the speedometer will read fast with the new tires installed. How fast? Well that depends on the percentage smaller that he chooses.
Your dads wheels won't bolt onto your truck, they need the center hub bored out, or you have to use wheel spacers.
Same to you, 20" wheels have no affect on the fitment whatsoever. You just adjust the sidewall accordingly to meet the overall diameter you wish to run.
In order for us to be of any additional help, you MUST specify what truck you own. A work truck? A 2wd? A 4wd? The offroad package, or not?
Let us know....