It took us 9 months from the start of the process to being approved. Then matched 2 weeks later. Then LO came come 2 months after that.
The process we didn't find stressful, it was more of a paper filling in exercise (that's how we treated it mentally as we didn't know how long it would take).
Our SW was lovely, we had building work going on through the process, and a lot of SW's would have stopped the application until it was finished, but he was very experienced and could see things would be complete by time we were approved.
References wise, they met with my Mum, Dad/Step-Mum, my partners parents, 2 of my friends, and had a telephone call with a friend of my partner. They also got written references from my partners siblings (they're not local).
I think he was just covering all bases, and got as many as he could so it wouldn't be an issue at approval panel!
It is very intrusive, from your finances (they want to see bank statements) to your sex life, to having access to a medical report on you done by your GP.
You have to sometimes bite your tongue, smile a lot, and sometimes I felt things were said to see how you reacted (not by our SW, but in the training, and also at the foster carer).
As people have said, you just have to think it will take time, you need to be patient and resilient, and know your life, past and present, will be scrutinised.