a good ol test kit is in order to find out how much oxygen and ammonia etc is in your tank, it costs a bit but one kit lasts a while.ask your fish shop for help, attually, dont. i use tetra brand kits and they work fine, some fish shops let you take in a cup of water and they test it for you, a lot cheaper.phone before hand to find out.taking the puffer back is a good thing to do, maybe a few other fish should join it in its return?maybe the live bearers(guppies, mollies and probally the baby fish).just untill you get sorted, dont buy anymore fish yet as you arent sure what your water parimiters are.
tetra aqua safe is what i use for water conditioner, it makes tap water safe and reduces stress levels in the fish, just follow the instructions printed on the back of the product for help, most other water treatment works also, it doesnt really matter what you use, aslong as it works in making tapwater safe for fish.a gravel vac is a good tool to help clean. have a look around for one you think is a good one. i also use a siphon tube to remove water. its a simple tube (like a hosepipe but never used for anything else but fish) and you suck at one end with the other end in the water, move you mouth out of the way quickly and the water gets sucked up and transfered into a bucket or such. it only works with taking water out, the siphon wont work going upwards.if the filter outtake makes quite a splash and bubbles are being made on the surface (not lots, but many) than that helps with oxygen levels, they is also a air stone you can add, but never using on myself i know nothing about them and you would need someone elses help here.