I'll let LBF tackle the explanation of KH and it relationship to pH, but I can help answer your filter question.
Originally Posted by johanna13
This is where I get very confused about the filter media. I was told to not replace the filter cartridges because that's where all the good bacteria is. but the cartridges are falling apart ..
Filter media is anything like foam, charcoal, cartridge, filter floss that you put in your filter to filter particles and to be colonized with nitrifying bacteria which cycle your tank. Your's is falling apart.
I assume, from having it in a cycled tank for months, that it's full of bacteria. Don't throw it out. Instead, install a new cartridge right on top of the old one. There ought to be enough room. After a couple of weeks the bacteria will be transferred to the new media. Then you can throw the old one away.