Fukien Tea are grown as indoor bonsai because they are not winter hardy in any but the very warmest locations - at least in Canada. Still, the health of your tree will improve considerably if you can keep it outside as long as the nights are above 50. As summer draws to a close, bring you tree back indoors - making the transition first at night and then for increasing stretches of the day.....or if you're like me, just get them inside when it gets too cold.
Winter positioning- Give your Fukien Tea the best indoor light you can give it, but keep it away from draughts - both hot and cold. If you don't have a spot that's bright enough, consider investing in at least a small grow light.
You'll also want to raise the local humidity around your bonsai, either with frequent misting or a pebble/water tray to raise the localized humidity.
The Fukien tea - like many plants (and most children) is not a fan of big changes, and this also applies to watering where once again I have to recommend that most difficult to execute instruction "evenly moist". This is not the same as "constantly wet". Imagine that you're holding a ball of soil in your hand and squeezing it. Properly "moist" soil would feel cool and damp. If the soil was "wet" you'd actually be able to squeeze water out of it and that would mean it has too much water. Let the top dry out a bit, water so that it flows through the pot, wait about 5 minutes and then water again. Never let the tree sit in water for more than 30 minutes.
Feed the tree from Spring to fall with a weak mixture of regular tropical plant food ( if you don't have bonsai food) and only use diluted liquid food on soil that is already moist. If watered with hard water the leaves can show signs of chlorosis which can be treated with iron fertilizer.
The best way to train a Fukien tea is simply by pruning, which will encourage a dense branch structure. Large branches become very brittle and so training a tree with wire can be risky.
When you repot your tree ( no more than every 2-3 years) be careful with the roots and keep trimming to a minimum, since Fukien Tea does not tolerate root loss as well as some other trees.
Finally, as to bugs: If your tree is not healthy it will attract spider mites, mealy bugs, scale and/or whitefly which you can get rid out using the standard controls , however long term, work on also adding more light and building up the local humidity to combat pests.