Depends on various laws. Around here all the craft breweries that do retail sales include kegs. YMMV.
Many can and do, but many more do not. Part of it is that a brewery that is not of a huge scale does not want to be sitting on inventory. Move it out the door to make room for more. Part of it is that kegs represent a decent amount of hassle to deal with on an individual scale. Deposits, the potential need for a tap/CO2, etc. No offense but the average keg buyer is not likely to return the empty keg as quickly or reliably as a bar will. Finally, the sale of beer on premise can often create strain with the distributor. This is why you'll see the beer sold on site no cheaper (and sometimes more expensive) than at another retail location. I'd ask each brewery individually. If they won't sell a keg then contact their distributor who would likely be happy to sell you a keg.
I know I've seen my favorite local brewery sell kegs while I was there, but I'm not sure what the laws are here in SW Ohio...
Depends on the state and then it would depend on what their licensing with that state is. Production breweries in Illinois cannot, just as they cannot hang a shingle outside of their facility advertising what they are. Brewpubs, taprooms etc are already licensed to sell at the consumer level so they can also hang a shingle.
