Pedicabs are, for all intents and purposes, illegal in NO. They grant MAYBE half a dozen special permits a year that are only good for 2-5 days each for various events.
There are a couple messengers but the work is slow. Before the storm there were maybe three companies and I believe there's only one now. The other two were ripping off the riders and once the storm hit the problem kind of took care of itself. Now the one company left is real slow, always. A lot of the work is legal and New Orleans (Orleans Parish) actually stretches across the river to Algiers so you'll get a tag from one courthouse downtown, over the river to the courthouse in Algeirs and the only way to get there is by overpass or the ferry. So the services "strongly prefer" that you have a car available. That and the CBD (central business district) is like four blocks by six blocks; tiny as hell.
Food delivery is an option but the jobs with the places that you're going to make good money (verdi mart, quarter master) are hard to get because they're steady and you make a good amount of change.
As for bike shops there are a few. Bike Michael's on Frenchman St. (good location, real central and easy to get to) The dudes are cool but the prices are a rip. Their main market is charging walk ins $25 to change a flat or someone ~$22 per wheel for a truing; if that's any indication of the rest of their prices. Another spot is Bayou Bikes out on Bayou St. John in Mid City. They're cool, the prices are on par with brick and mortar bike shops. If you roll in with a reasonable internet price the dude will usually come down to what it would be with shipping... he's cool as long as you're not a dick about it. There are a couple one man ops, one on Magazine @ Napoleon, guy's name is Mike. It's a tiny shop, normal prices and he does good work for reasonable rate. If you're in the area and you need someone to do your build I'd take it him. If you just need parts then get them online, nobody really stocks anything.
Check out nopolo.org and nolabikerace.com for info about stuff around town. There are maybe a dozen dudes who ride fixed on a regular basis and they're all cool; nobody's got any attitudes.