No, a 29 is not big enough for a ribbon eel. They are not a good fish for a newbie-or even many experienced feepers-they are known to be difficult to get feeding and maintain. Eels are also very good at eating crustaceans--the shrimp would likely become a snack.
Mandarins should not go in newly setup tanks. Sorry--I know how pretty they are, but they need a sizable population of pods to feed on while juveniles. Most will acclimate to prepared foods, but this takes several months. In small tanks, they will clean out the pod population in short order, then slowly starve to death. Mandarins and scooters are in the same family, and both are prone to starving, especially in new and small tanks.
In general, I urge people to wait until the tank has been stable for a minimum of 6 months before adding corals. They are more sensitive to water conditions that most fish, and when they die, they can be a major pollutant. Remember--the nitrogen cycle is not the only thing that must be balanced--it's just the one we can test and track.