Is it difficult or complicated to care for bonsai trees?
Keeping them alive is not complicated but they tend to be relatively delicate due to the lack of soil; you have to make sure they don’t get too much or too little water. You also have to know what conditions they like, which differ from one species to another. I had one that loved being outside and languished in the sunroom in the winter. “Training” them, of course, is an art.
Those little bonsai trees I see for sale - are they already ‘‘trained’’?
I had a couple of bonsai trees and, while they are nifty, I killed them both.
I think you have to be a little more careful with them than a normal plant. At least, I had to be (and failed!).
Not difficult or complicated at all if you don’t mind them dying after a few months. I am no expert but I’ve killed a few bonsai. It depends on the bonsai. Some are trees, some are shrubs, some are something else so they all want diffferent care.
My wife keeps bringing them home from the guy at the framer’s market who sells them. I contend that they aren’t really bonsai. He, and my wife, contend that any plant in a small bonsai pot is a bonsai. I can keep one in three alive for more than a year.
I think bonsai trees look neat, but I don’t have much experience in caring for houseplants.
Disaster lies ahead. 
I am no expert on this subject, but I think there are relatively simple bonsai-like projects that can be done on woody tropical plants, that would take to indoor conditions more readily than “traditional” hardy trees and shrubs.
It depends very much on the species. I don’t have bonsai trees myself, but my father has quite a few. He says jade trees are about as close to unkillable as you’ll find in a bonsai, and they’re pretty easy to train.
(Of course, this is also the man who adapted a server rack into a rolling bonsai garden with its own modular lighting system.)
Remember something, bonsai are NOT houseplants in general. They really should spend most of their time outside in the conditions that the particular plant prefers.
Bonsai should really be outside most of the time.
Also, I would get some practice on caring for hardier plants before getting a bonsai. There are tons of easy to care for plants, and once you feel comfortable caring for them and learn to “read” their signals, you’ll be in a better position to care for a bonsai. I wouldn’t say (all/most) bonsai are an “advanced” plant, but they tend to be “moderate”. I would practice with plants that are easy.
It took being in a house fire to kill my Mom’s jade tree. She found it dried out in a pot in the house Dad got when they got married in 1949, the original plant had been growing in a pot in the upper center window landing since about 1900 and was about 6 feet tall and 6 feet around when she found it. She ended up cutting it severely to less than half the original size and kept it trimmed down [and rooting and giving away the cuttings] until it died.
Wax plants are also very sturdy, hers survived the fire :eek: [though the blossoms will drip nectar if they are abundantly watered.]
I’ve got a juniper bonsai that was a house warming gift from a friend. We’ve been in our house 10 years and some months now, so it has survived my sporadic care for that long, inside our glassed in porch on the north side of the house. The first bonsai I was given only lasted a few months because I didn’t realise how little rain it was getting up against my house wall and it dried out and died. I made sure I didn’t make this one suffer the same fate.
I have never trimmed the roots, or changed the soil mix and have only trimmed a few branches just to keep it from elbowing out the other pot plants it shares a shelf with.
This example is the same variety but somewhat grander than mine.
Without knowing where you live, or your gardening background, any answers are really a shot in the dark, but I am going to suggest you look into Adenium plants. Especially Adenium arabicum. I can’t post pictures here of my plants, but you can Google pictures for examples. A. Arabicum can be kept quite small, and require normal watering in the summer, and none in the winter. I bring mine in when night temps get into the 40’s. They flower too! If you send me a message I can send photos.