yes, similar experience - I had some doors that really needed to stay closed but many staff just couldn't get into the habit of closing the doors after opening them to pass through
I'm not sure about billions for that, as it's more difficult to estimate than the population by climate, but I'm sure (based on my previous business experience) that there are many people who don't think it's important that doors are kept closed and/or assume that doors that need to be closed will close automatically
Yes, there are billions of people in the world who aren't familiar with how air-con works, including those who haven't spent much of their lives in hot climates, who wouldn't see the issue here.
I used to do a bit of gardening here, and everyone thought I was crazy. At the time, I thought they were crazy for thinking I was crazy but now I understand I was indeed crazy.
It's ridiculously hot outside, there are all kinds of creepy crawlies all over the place, and there are millions of locals standing ready to do such chores for a pittance.
If you want to do some physical activity, play golf, and bring an umbrella.
As for maintenance inside the house, there is no chance of the authorities questioning this, as they won't know you're doing it, but if you pay someone else to do it, you will have more time for golf.