All living things are eaten by other living things and your bonsai are no exception.
A healthy tree will be able to shake off most diseases, keep it well fed use sharp tools to make cuts that will heal over better and you should have very few problems.
The Type of insect taking an interest in your tree will vary with where you are in the world, however your response will tend to be the same. Man's ingenuity has provided us with chemicals to really put them off their lunch. Some of you will favour organic methods of growing your trees, however good these methods may be their response time will not be as fast as a good dose of Malathion.
If, in the joints between branches you see fine white cobwebs, you may have an infestation of red spider mite. They, as their name suggests look like spiders and make a web like substance. They're microscopic, just visible with a magnifying glass. That will not however stop them killing you tree. They tend to be associated with indoor trees, as they prefer a warm dry climate. Your local garden store should have something for them to drink (terminally). After that, spray (mist) your trees regularly with water, and see, what I have to say about Humidity.
I should start by saying that not all fungi are harmfull to your trees, all plants have a symbiotic root fungus called Mycorrhiza which benifits the tree. It can usually be seen as a thin white sheet around the roots, on repotting and is particularly noticable on Pines, it is as I said benificial. However most fungi will kill your tree, or disfigure the leaves.
Fungi enter your tree through wounds and particularly those wounds below soil level, so when repotting your trees the first watering should contain a fungicide. Other fungi, such as mildew or blackspot will attack your leaves, disfiguring them and greatly reducing their ability to feed the tree, regular spraying with a fungicide will help to prevent this.
High Nitrogen feeds promote rapid, soft growth and this, if damaged may allow scab to enter, so watch out.
Scab itself is typified by the shrinking and drying of an area of bark. If you are the victim of such an attack you will find a remidy, usually a spray in your garden center.
Assuming you,ve stopped the attack in time, you might consider applying a 'Dead wood' effect to the damaged area.
Cats are not a problem if dealt with in a sympathetic and understanding manor.
My own late moggie had a spot on my Bonsai racks where he liked to sun himself. I left a space for him, aren't cats quick when you start to water your trees ?.
The last thing I would suggest is that you keep you children away from your trees, however very young children will mimic their parents as part of the growing process. If they see you working on a tree they may decide to 'help' you, with perhaps disasterous results for your trees. Keep your tools away from them.
© Allen. C. Roffey 11:21 02/07/2005