It varies. Some rescues use a network of home-checkers who work with various different rescues, others only use their own.
In my experience, they all check/ask about sleeping arrangements, veterinary provision, local walks. They also generally ask about work commitments, how long the dog is likely to be left, if at all and usually want to meet all members of the household. They will want to see your garden to check for fence height/any gaps in fencing.
We’ve always had another dog at home, which I think makes it a little easier, as they are able to see your set up and assess it’s suitability. We’ve never had one bring their own dog, but I have heard plenty of people who have.
I believe some rescues are doing video home-checks at the moment. Not sure how they work, unless you have to walk around your home with a laptop or phone camera on! 
I have had rescues going back 30 years and have never had a bad experience with a home-checker. They’re usually lovely people who just want the best for the dogs they are helping to rehome. Quickest and most cursory one was from the DogsTrust, which was still the NCDL back then (showing my age now). Last one (8 years ago) was a local home-checker from a national network of volunteer checkers, acting for a small independent rescue. She was more interested in our house’s architecture and age than anything else, although still did the main checks re fencing, bedding, vetsetc and ticked off her list as she was chatting with us.
Nothing to be worried about at all.