Hi Lewis 
To answer your four questions, no, no, no and yes (depending on the path you take).
There is an offshoot thread from this one re weight so clearly not everyone is super skinny. Some clinics have a max BMI I think.
I'm most definitely not rich, but I have to admit I do wish I was in a slightly better position financially. I went to Denmark for treatment for a few reasons, but not least because it is a lot cheaper than the UK. My IUIs each cost £800 per attempt including the donor sperm, plus £120-£300 travel costs (depending on day I needed to travel plus school holidays making travel/hotels more expensive).
I'm 36 weeks pregnant now with no savings which is a bit scary but I'll muddle through with maternity pay, odd bits of freelance work and hoping I'll be eligible for some child tax credits until January when I intend to start working 3 days per week at which point I should be able to receive working tax credits. Then once free childcare kicks in I should be able to make ends meet without frittering away tax payers' money any longer 
Re approval, your fertility clinic will go through an in depth medical history with you and go through a counselling type session to establish whether you are in a reasonable place to manage pregnancy and a child on your own. If you have any medical conditions you will need a letter from your GP confirming that none of your conditions should be a reason for you not to get pregnant.