I am not quite sure what you are asking in the first question, but I think you want to know where the media you will add should come from. It makes little difference. I generally like to use something that can fit in the new filter- the filter you will be using for the 29 - simply because the bacterial colonies always grow better when they have a place to colonize that has a ready access to the ammonia - ie: moving water through the filter that brings a constant souce - as well as a good supply of oxygen -something that is needed in the nitrogen cycle to process the ammonia. Without oxygen, there will be no cycle.
You have several options - as far as how to season the new media. The best way would be in a working filter - to supply the constant flow of water and oxygen. If there is no room in the qt tank's filter to add anything else, what about adding one of those aquaclear filters to the 10 gallon and set it going, full of media? I have had an aquaclear and a Penguin 110 running at the same time on a 10 with no bad effects - the guppies did just fine. I gave them some plants and rocks to hide and swim through and they were happy little guys.
So you stuff the aquaclear full of media and set it running on the 10QT. Let it run for 2 weeks, feeding your tetra fish the full amount of food - do not skimp on the food. Change the water out as you normally do - treat it all the same. Being a tropical tank, and thus warmer, it is even better!
At the end of two weeks, set up the 29 with its respective filters, heaters, bubblers, etc all going. I think I would then see if you can split the filter media from the original filter that is in the 10 gallon. Take a bit of whatever you have from there - 1/3 - 1/2 of it or so and drop some of the stuff from the newer aquaclear back into the qt filter to fill it again. Then take that aquaclear filter and hang it over the side of the 29 and set it going, too. Stuff the media from the qt tank into it or the new filters or anywhere you can stuff it.
Add your little goldie and test away. Do not wait more than 36 hours to add the goldie after you move the filters (media) - the sooner the better. You need to feed your bacteria!
If you take some - up to 1/2 of the media from the 10, I doubt that you will cause anything more than a 12 hour bump in the cycle. It is not a big bio-load, for the fish do not create so much waste that the ppm will jump too much within a day or two. That is plenty of time for the bacterial colony to respond and regrow to fill the needs of the tank. I do not think you will have any worries there. If you do see a bump, it should be a small, transitory one.
Do not put anything under any gravel. You are setting it up to be populated by many of the small critters that ineveitably live in the detrius in a gravel based tank. It will not recieve the proper oxygen or water turnover to properly colonate with beneficial bacteria. If you wish to lean the 29 cartridges up against the side s of the qt tank, you can, though. It is not as efficiant as media in a filter, but should work fine, also - particularly if you can lean them where the overflow from the filter will hit them.
I have never known bio-zyme to do anything, but since you have it and I love to be optomistic, why not add it when you start the 29 going? I have never heard of it doing anything bad, so take a chance that it might do something good!
After your 29 is all cycled and going, you might want to consider doing what I have done. I drop a small bag of lava rock, ceramic cylindars, bio balls or some such thing in the back, behind a decoration or plant and just let it be. Whenever I need a "seed" for a new filter or tank, I can pull one of these bags out from where they are stashed and use them. It helps set up an instantly cycled qt tank, or replacement of a blasted cycle when treating with meds. They are only good if the tank is healthy. After using a bag from a tank with potiential disease, it should be boiled and recolonated.