I am not sure on the quantity of beef liver. I would offer him a tablespoon and see how he reacts. I also do not know how long you should offer it; perhaps until he stops stumbling. @Eggcessive may have more information.
If my rooster was in this type of distress, I would offer him a small...
You are doing great. with the coop and run, just make sure you get every nook and cranny with the spray. If you are using a spray, make sure you use it according to the label, some need to be diluted before use.
As for the liver - you really don't need to prepare it - they will love it raw...
If your rooster is already feeling down, bathing him may cause more stress. The poultry dust is a powder. One of the people on this forum @Wyorp Rock suggest putting the powder in a sock and using the sock as a powder puff. Puff his vent and under his wings.
If he has mites, they are...