first of all, HI and welcome to the forum! You have alot of questions, and i will try to answer some of them. 8)
first of all, if i understood correctly, you are "cycling" your tank by adding waste that you remove from your other tank with a turkey baster? IF this is what you are doing, you should stop. This is not good. Here is a good thread on the different ways that you can effectively cycle your tank: http://www.fishforum.com/viewtopic.php?t=3738
I suggest you read it. I wouldnt cycle your tank with the betta IN it, so next easiest way would be to just drop a few flakes in the tank twice a day or so, until your water readings show 0 ammonia, 0 nitrite, and <10 nitrate.
which leads me to the next issue. you should have a test kit.(if you dont have one) you cannot really effectively cycle your tank without knowing what your water parameters are. i recommend that you purchase a liquid test kit (API) that tests for ammonia, nitrite, nitrate, ph, etc.
in answer to your question, if you cycle by adding food, it will not just sit there, you only need a pinch, and it will dissolve and turn into ammonia.
you should never do a 100% water change, especially while you are cycling. if you arent cycling with fish, you dont need to do any water changes while cycling. after cycling is complete, you can do a 25% water change and then add the fish.(acclimate him though...don't just drop him in.) then you should perform routine weekly water changes with gravel vacuuming. 10-15%.
the good bacteria that build up in your tank will grow everywhere. primarily in your filter media. if you have a HOB filter, there should be two "spongy thingys". one is a carbon filter, that you can change every month(? or whatever is recommended) and another is white. the white one is where your bacteria will grow. you should never change this one. the bacteria will also grow in your substrate (so make sure you have enough) and on decorations, etc.
your fish should not have an aversion to the filter, they are pretty quiet. if for some reason, maintenance, etc, that the filter has to be off for awhile, that is fine. the fish can survive for a day or so without filtration, but its the oxygen in the water that becomes the issue. as long as you stir the water several times a day to promote gas exchange, the fish will be fine. or if you use an airstone, that will work too.
sorry for the long explanation, but hope some of this helps you!!