The white things could be wooly aphids, a pest. I can't diagnose from the pictures. If I'm correct an insecticide is needed.
You could try a basic homemade oil spray. Use one gallon of water and mix in 1 tablesp of vegetable oil (cooking oil), I tablesp of mild dishwashing soap (like Ivory). shake well and place into a spray bottle. Add a cap or two of rubbing alcohol to the sprayer and spray the tree, Do not do this in the sun, the oil and sunlight can burn the tree.
"How do I fix the roots?" The roots are pruned and raked out gently with a chopstick or similar implement. The tree is then repotted into a good bonsai mix. This is done in the spring and it takes some knowledge and experience which brings me to my next point.
You have to read and learn about bonsai. In addition to this forum there are good websites like bonsai4me and evergreengardenworks and others with good information. Read through the posts in this forum. There are books at the public library, Videos on you-tube (esp the Bonsai Art of Japan Series). The best thing is to join a local bonsai club.