Can I, for example to remove all the grass and make rock garden on MY yard?
I'm not American so I'm naive questions.
Privet. Like Russia, the country is so big there are different areas, and city areas have different rules than rural areas. Different cities have rules different from other cities. Different states have different rules, but city rules seem to rule supreme regardless of state.
Like Russia, here there are different areas of topography. There are mountainous regions, foothill regions, just hilly regions, flatland regions, almost tropical regions, e.g., Florida, which I don't think you have in Russia. There are desert regions and abundant greenlands.
There are metropolitan areas and rural areas. There are suburban areas adjacent to metropolitan areas. Probably the same as in Russia around Mockva.
The article in the post was about a region with complications. It's a metropolitan area in a region without a large natural supply of water. Los Angeles' water is piped in from other areas. (The 1974 movie "Chinatown" explores this.) So there is a conflict if there is a lack of rainfall. No rain equals brown lawns. Metropolitan areas like pretty lawns.
It doesn't matter if it's your grass on your land, nor if it's drought. Some idiot from the city may or may not cite you because they don't like the looks of your lawn. It's California, which a lot of US citizens consider a crazy state; besides which there are idiots in every city everywhere, even Moscow.
Yet, because of water being piped in from far away, Los Angeles is frequently faced with not having enough water. Therefore, the residents frequently face pleas to use less water. That couple tried to conserve their water usage, but some over zealous city official didn't like their brown lawn.
It's too early to tell what the outcome will be. Personally, I'd think it will amount to not much at all, but you never know.
Can I, for example to remove all the grass and make rock garden on MY yard?
As far as I know in most cities, most likely. I've seen city yards done this way. Our present front yard, however, is .5 an acre. My husband frequently threatened this after mowing the yard of our previous .25 acre yard on days of 95F with 90% humidity.