Welcome to FishLore! It's geat to have you with us!
Don't pay any attention to what the box says. You are absolutely correct about the bacteria, and don't need to change the filter media unless your water flow back into the tank is affected and sluggish. Then you can try "swishing" the media in used tank water to try and get some of the crud off. This should be able to work for a good while. If that doesn't work or the media is simply falling apart, then you can cut some of the media and place it in the new media if you have the type that's like a bag where you put the carbon inside. You won't be able to do this if you have the type that is all one piece. I have had some of my filter media over 6 months and they are still going strong.
I'm not sure, but I think all 3 of those products treat for
chlorine and chloramines, and if that is so, you don't need to use all 3 of them. My preference to use a basic water conditioner which only treats for chlorine, chloramines, and heavy metals. I don't like the ones that have additives like aloe or stuff for their slime coat. Save the amquel plus for when you have an
ammonia and
nitrite spike. The amquel plus may actually hinder your cycle right now, because it also deals with ammonia and nitrites. Since your tank isn't established, I would not use it unless absolutely necessary right now. So in answer to your question, the answer is no, you don't have to use all 3. Just use 1 water conditioner at a time.
Puffers are so cool! I have never owned one, but some day I will. I think you need to do some research on your baby. I know they love snails, but not malaysian trumpet snails. Their shells are too hard for the puffers to crack, and it could break their teeth. You will have to make sure and feed him a lot of pond snails to keep his teeth ground down. They will continue to grow, and could actually grow back into their skin if not kept under control. Some owners actually clip their teeth. I'd rather let them wear down naturally.

Anyway, you also know that puffers are brackish water fish, right? I've got a couple of links posted below to get you started:
http://www.pufferfish.co.uk/aquaria/...fish/index.htm http://fish.mongabay.com/species/Tet...roviridis.html
P.S. Can you please post your ammonia, nitrite, and
nitrate readings?