The brown dead growth on the inside is most likely from lack of light. if they are completely dead i would recommend removing them. This will allow for better air circulation in the tree and could possibly encourage back budding in that area.

As far as soil mixture it depends on where you are located as local weather patterns will cause the soil to stay wet for a different time frame. Example would be that a mixture used in Florida, if used in Wisconsin will kill the tree as it will stay wet too long. That being said I think the mixture stated will work out alright for you, I'm going on what works in my area and your yearly weather probably is about the same as mine. The soil its in now is probably inadequate as is most soil trees from low grade nurseries and flower order sites have their Bonsai tree's in.

Make sure the soil isn't watered too often (only watered when the soil is almost completely dry, But NOT completely). The soil should only stay wet for 3 days at most before having to be watered again or it is retaining too much water. Also keep in mid this tree will have to kept outdoors during winter or it will eventually weaken and die.

I recommend going to your local library and reading up on as many Bonsai books there as possible. That should help clear up a lot for you.