Definitely remove all uneaten food and should be done shortly after the food goes in the tank. The puffer does need to come out. Not a good fish for cycling. Though hardy once established in their environments, they do poorly with rising levels of toxins. BTW...any crustacean is not safe from any puffer. What's the porky???
I'd suggest doing 10% water changes twice a week for two weeks to down any waste the puffer and excess food has built up. Granted many animals can adapt to slow rising levels of toxins, but even they can fall to fast rising toxins. The more waste, the more uneaten food, the quicker the ammonia will rise. Don't be surprised if you lose the snail and hermits. Crustaceans should go into an established tank. They do not do well with ammonia. You could try to protect the ones you have by adding a supplimental bio additive like NitroMax Marine. The damsels are fairly hardy and commonly used to cycle marine tanks.
I'd wait until the water is fully tested (ammonia, nitrite, nitrate, pH and SG) before adding more live rock. If there is a good amount of ammonia and/or nitrite, it could kill some of the bio on the live rock and add to the ammonia. If it's at least 40 gallons, adding some type of rock is fine. Many people use lava rock and lace rock to add to the live rock. It will eventually become just as impregnated with the same microorganisms the live rock has. It will become live rock. Makes it a bit less expensive too
Feeding should be extremely sparing during the cycle's establishment. With live rock...about 3 minutes worth of food split into two or more feeds twice a week. This will help keep ammonia from rising too fast yet still allow the fish to eat. If they refuse to eat, it'll most likely be because of nitrite levels. Just stick it out. They'll do fine. There are many species of fish that can go a very long time without food. Water condition is most important when it comes to keeping fish alive. Once the cycle is established, the same feeding pattern, twice a week, but about five minutes worth of food split into two or more feeds. Fish will eat and graze on natural growth in the system. Two days a week adding food is enough unless the rock is lacking natural growth such as macro algae and copepods. If you have more active/hyper fish like tangs and wrasses, add a day.
Once the puffer is gone and other arrangements made, then yes...kick back and let it do it's thing. You can do 10% water changes once a week or 15% once every two weeks after those few extra water changes are done and keep it routine.
How big is the tank? Describe it...type filter, total wattage of lighting, what do you plan on having??? etc.
