DirtyOldDuck

Recipes 

Although it doesn't answer the question of trademark, most state's Secretary of State maintain a database of businesses registered to do business in the state. You can do a business name search for "Arch City Brewers" on the SOS's site for Ohio and find that there are no business with that registered name. By the way, I think the Lazy Greyhound name has a lot more character - just my opinion (full disclosure - I use "2 Bad Dogs Brewing.")

dkmitg

Recipes 

Most competitions don't allow any identifying marks except for the number they assign you to avoid bias judging anyway but im not sure how this contest is run

BarefootFriar

Recipes 

If it's in the archives, then it may be public domain, in which case you can reproduce it however you want. In literature, it's the life of the author plus fifty years. I don't know what it is in art (including photographs). A quick Google may answer that.