The "Trouble Alert" comment was a nod to the "Trouble Alert" used by the Super Friends on the Saturday morning cartoon Super Friends (1973).
Johnathon Schaech reprises his role as Jonah Hex. He previously played the character in The Magnificent Eight (2016).
Sara tells Rory "Why don't you mosey on in there? Have yourself a good time." "mosey on" is to stroll, walk leisurely, without any special purpose. But as it is revealed later, Sara's instruction to Rory was to start a fight in there so that Turnbull comes out of the saloon, then this is not the correct use of the phrase "mosey on".
Jonah Hex says that he and Turnbull wants each other "pushing up daisies". It means "to be dead and buried".
"this ain't my first rodeo" is mostly used in instances where a less experienced person is trying to give advice to a more experienced person, and is meant to establish superiority in a friendly leg pulling or a domineering manner.