You need to register as self employed. Then you have a year of reporting income and expenses, if after a year your business is not turning a good enough profit they expect you to seek additional employment, but hopefully a year will be enough to get there for you. You report a change that you are going self employed.
As regards studying, you have to call them because there is no place to report it on the journal, so you have to call them. Then they will ask for details of your course, any hours studying are deducted from your hours you have to do work search if not working. So eg. You can study 16+ hours then don't have to work at all, or study 8 hours, work 8 hours, study 3 and work 15 hours, etc. but that time can be working on your business, which you don't have to get proper earning from until you've been self employed for a year, during which time you get full benefits, minus anything you earn over the income threshold. So if your income threshold is eg £300 because you are a parent, then you keep 100% of the first £300 and then a percentage there after is deductible from the benefit.
It's probably a pretty smart move to start a business and get additional training during that time as well, whilst knowing that you'll get that UC. Yes not generous being on benefits, but if you can earn something, improve your skills and build something that will keep you employed and where you get to chose your own hours long term then I would do it.
When they are 5 years old you have to work 25 hours I think, and it's 35 hours plus later on, so if you can improve your skills and build a business now, that's going to make it less scary when those hours go up, you can just increase your hours doing whatever it is your trained to do.
It worth looking at what there is a gap for in the job market, if there are loads of nail shops going out of business, might be a bad time to train to do nails, but if there's a shortage of childminders or electricians, might be worth considering different occupations that are highly in demand where you get to set your own hours too