Only you would know the cycling of your tank....there's not a lot of details here to really tell.
For instance, having lots of cured liverock and live sandbed would help the cycling, as well as adding an over-the-counter "cycling" solution that promotes good bacteria growth to start processing the ammonia, nitrates, and nitrites.
Also, did you put most of these fish in all at once, or did you just start out with 1-2 fish?
Another factor you must consider is the fact that your tank (30 gal.) is actually quite small for the full cycle or water parameters to become "stable". Remember, the more water capacity (such as a 100+ gal tank), the less you have to worry about water conditions and ammonia spikes. If you have a 50 gal or less, such as a nano-tank), water conditions must be monitored almost DAILY. To me, it seems like you will have a huge bioload with the puffer (puffers are generally messy eaters).
My suggestion would be to return a few fish to the LFS you got them at and get store credit. Explain to them the situation, and when your tank is fully cycled and water conditions are stable for a period of about 2-3 months, then I would start adding new livestock one by one. You can probably keep 1-2 fish while you are doing this, but the amount you have is probably a little too much for where you are at in the cycling process.