... I’m worried about the people that try sue because ... I do the treatment good and they try find something wrong.
As a self employed person, you need to develop a thick skin because there’s always the odd chancer who will feel entitled to get something for nothing and refuse to pay for the service citing some made up non issue. If you know you’ve done a good job, stand your ground and continue to request payment in full. This is more difficult when you’re mobile and in someone else’s house. Thankfully, it doesn’t happen too often and most hairdressers learn to develop a sixth sense for these types of clients.
Simply not liking the finished cut/colour isn’t grounds to sue someone in court so the most you will lose is the cost of the service if they refuse to pay you. You can sue the client for breach of contract but the cost of going to court usually outweighs the loss of revenue and so most hairdressers let it go.
The good news is that there are very few cases in the U.K. where a client has successfully sued their hairdresser.
Obviously if a client trips on a wet slippy floor and breaks a bone, that’s no different to a customer tripping in a shop and suing Tesco.
Generally, they can only sue for mega bucks when the hairdresser has made a serious mistake that has resulted in physical harm to the client, such as using strong bleach on the scalp and causing a weeping scalp or performing a colour without doing a skin test and the client suffers a severe reaction to the colour. A competent hairdresser is unlikely to make these sorts of mistakes and even if you do, your insurer will deal with the complainant.
As
@BannerPenguin says, providing you have insurance cover, you really don’t need to worry. We do get the occasional poster on here being threatened with court action. It’s generally hairdressers trying to do work on the side and not bothering to purchase insurance who get into a pickle.