A bank may require an appraisal and inspection, but a buyer is not obligated to get a mortgage. If the buyer needs a mortgage and the bank requires an inspection, the buyer is responsible for the cost.
I've asked sellers to do inspections before. It's always been in situations where the house has obvious issues and I'm not willing to spend potentially a thousand dollars to find out how deep the issues go. One house that I demanded it for ended up having six figures in moisture damage. It ended up foreclosed twice because new buyers weren't as aggressive as I was.
The buyer is responsible for any and all inspections. The seller is responsible to tell you what they know about the property, what repairs have been done, what problems still remain, etc.
The inspection will let you know about all the systems of the property, etc that the seller may not know about, but you what to know about before buying.
Buyer
you as the potential buyer would definitely want an inspection
the city....permits need to be filed by the builder or general contractor....then the inspector checks the work...wiring , duct work, pipes, etc before the walls are put up...then they check the walls, outlets furnace , etc etc etc
You are should you need it. You do it directly or indirectly throught the agent/seller. If your bank requires it, you pay for it.