It has been more years than I care to remember since I did my initial carpet cleaning training.
It depends where you do your training, as to what they tell you. for instance a manufacturer based training course will encourage you to buy only their products, and machinery. A national training course will be more un-biased, and not leave you with much clue where to go, the only way for a happy medium is to go out with a cleaner not too far (or too near) your area of work, and see how he/she does it.
Furniture removal is down to you. I always tell the customer that I will not move anything that will break or give me a hernia, and I will not move huge TV's etc. All have been fine with this. I move beds from one side to the other of the room, but only if they don't seem as though they will break. Generally I go round beds....
Insurance... there are a few companies who advertise on here, and all you really need is treatment risk as an additional option, because that covers you for what you are working on... Normal liability insurance does not.
Other than that, just read previous posts on here, use the search function at the top, and have a good look round... Most questions have been answered in 1 form or another on here.
Never be afraid to ask questions though as you will get a variety of answers to most you ask.