Okay, new circumstances, you may or may not be done cycling already...
1. Take the puffer back -- the rest of your fish can probably survive a partially cycled tank -- the puffer won't be a good choice in the short or long run. Get store credit, they should have never sold you a puffer for a 30 gallon anyway.
2. Buy test kits, preferrably Salifert, for ammonia, nitrite, nitrate and confirm that you have no ammonia or nitrite in the system. If you do, start changing a 5 gallon bucket of water every day until you don't. You may be completely done cycling, you may not -- you need to know with certainty.
I would hold off on feeding anything that's relatively "messy" like frozen shrimp until you know your cycle is complete and your filtration is adequate (as in, no ammonia or nitrite detectable, no nitrate buildup in the system over time). I'd stick to flake just because it's easier to feed sparingly and easier to remove if there's any left over.
You may kill some fish, we've all done it for the most part. The toughest part about saltwater tanks is adding fish slowly enough to keep the system working well.
For perspective's sake, I have 5 fish (one tang, the rest are all no larger than the ocellaris clown) in a 125 with 40 gallon sump, and at most will add one more. My skimmer is probably double the size I need for my tank size and low bioload, I have a refugium running full time with lights over the macroalgae to help with filtration as well, and I have a lot of flow in the tank to maximize the filtration capacity of the LR. In other words, I probably have at least fifteen times the filtration / dilution capacity you have with the same number of fish -- so yeah you're really pushing it as far as I'm concerned on bioload.
Just fix it the best you can now, and make sure things stabilize in a good spot (no nutrient buildup) over a couple of months before adding anything else other than additional filtration devices. Be ready to make water changes because I think you're going to need plenty of them...