How do I replace the fleece/fur on the underside of my western saddle?

I recently got a very old western roping saddle on the side of the rode in a free pile. It was full of green mold but that problem has been resolved and the mold is done with, I don't know if it will stay away so any suggestions will be helpful. I sprayed it today with Lysol because Lysol is supposed to kill mold. Secondly the Stirrup adjusters were rusted on I was told to use an SOS pad and I did and it worked very well, but I was wondering if there is anything that work work better because the pad was very torn up and unusable before I was finished. Thirdly, the biggest one the fleece or fur(if you know what it is called please let me know!) is falling off a lot. It is also filled with dirt, green mold, and dirt, and who knows what! I am looking to replace it, but if there is a way to replace it myself and not spend the money on someone to do that for me would be amazing. I am very handy with sewing, carpentry and all of that stuff and I have access to the materials that I think I may need. I do not, however know how to do the tearing it out and replacing it into the underside. I was also wondering(just thought of it) if there is anyway to get rid of bite marks from horses because my cousins horse decided to taste my saddle. Thank you so much!!!