Yes, one of the best ways to manage black knot is to prune out all the "knots" (cut 6 to 8 inches below them). Fungicides can be used in combination with this pruning/sanitation and applied at the white bud and petal fall growth stages. More information here: Black knot, MSU Integrated Pest Management

This is a great publication from Purdue Extension that has images of what the "white bud" and "peal fall" stages look like and recommends using the fungicide Chlorothalonil: Managing Pests in Home Fruit Plantings

Sure thing! I would wait to prune until the dormant season (late winter). Pruning right now can create open wounds that would be a site for further infection from other pathogens or pests - best to avoid that! The fungicide will be applied in spring based on when the tree is at the "white bud" and "petal fall" stages (reference images in this publication from Purdue). Fungicides are used for preventing further infection. You can imagine that they sort of create a barrier on the foliage and branches that prevent fungal spores from taking hold. They don't really "cure" the tree and that's why it is important to use pruning/sanitation in combination with them to limit how much pathogen is present.

Yeah, I have also heard you can burn them. Otherwise you can bag them up and put them in the trash. Avoid composting because those "knots" can still spread the pathogen. Also, when you prune be sure to sanitize your shears with 10% bleach after each cut, and definitely before pruning on another tree. 

The fruit should be okay to eat. Black knot usually affects the branches and not the fruit (maybe fruit spurs).