( Earth can support human population of 528 million only, for all flora and fauna are to have equal room for their own progression. And we are currently around 9-9.5 billion)

This sounds bs

When there is nothing that can be gained from others ( sufficient and equal distribution of resources)

This supposes that all "needs" are met, but "wants" are still going to be "wanted" by people thus the greed persists. Sure, I could eat the free bread provided for me by "the state" or "the people" depending on who you ask and that's technically sufficient for my caloric intake for the day, but I want rye bread, and some rye whiskey to go with it. What I "need" is calories, but what I want is a specific taste.

On that matter, nobody "needs" rye whiskey nor any other alcohol, are those now blacklisted as being for the bourgoise, "you only 'need' calories and water блять?" Who gets to define "need" and "want?" If I decide I need alcohol, do I have to ask permision from the комиссар before it gets provided for me instead of just "going to the store," considering there's no more stores or money? Do I have to hope I have something in trade wanted by the liquor store owner (considering he doesn't "need" anything all trades would have to be done in "wants" right? So I'd have to find a liquor store ~~owner~~ (whoops no more owning either, I guess I mean liquor store part owner, or proprietor, maybe hoochmonger) that happens to have the same interests as me and trade something he wants, but then how did I get that to trade in the first place?)

Each married woman to have maximum of 3 children, with a minimum of 7 year gap

If communism is a stateless society, how do you enforce these draconian birth control laws and control those woman's bodies? How do you force nonmarried women to abort or pill if they want a kid but you say they can't have one, and how do you enforce a married couple who accidentally gets pregnant before you let them or decides they want more than 3 kids? And should we even do that? I get that the goal is to stem overpopulation (which I've been assured is a myth btw, not sure I buy that though), but is it morally correct to police (anyone's really, but) women's bodies like that? Frankly I don't think so.

And let's say they get married and have a kid by a fairly young "27," that puts baby #2 at a min of 34 and #3 at a min of 41. If they have trouble conceiving and don't get #2 for a few years then #3 is getting into sketchy territory, turns out:

A pregnancy after age 35 automatically puts you in the “advanced maternal age” (AMA) category (but many are still successful so don't be scared!)

Fertility rates trend with the average number of eggs a woman has at any given age. In general, you begin puberty with between 300,000 to 500,000 eggs. This number drops to around 25,000 at age 37 and continues dropping to 1,000 or fewer by age 51. How does this look exactly? Well, the likelihood of becoming pregnant naturally (without medical assistance) after a year of trying is as follows:

<30 years old	85 percent
30 years old	75 percent
35 years old	66 percent
40 years old	44 percent

Even if you have a lot of eggs and you’re in your 20s or early 30s, your chance of getting pregnant in any given month is 1 out of 4, according to ACOG. By the time you reach 40, only 1 in 10 women will get pregnant each cycle.

It's entirely possible to get pregnant up until menopause but it is increasingly unlikely, so a woman who wants 3 kids would really have to start younger than their mid 20s (and many do, but they're commonly accidents.) However with women not just being wombs and dishwashers anymore many choose to focus on a career at first and get to the babymaking later, meaning they're having #1 later:

Women in the U.S. are more likely to delay motherhood now, compared to decades past, according to The Centers For Disease Control and Prevention. More than two decades ago the average age of a first-time mother was 24.9. Now, the average woman or birthing person is having their first child at 27.5 - a record high in the country.

Oddly this ends up being somewhat racist in that it affects specific POC more than the rest of the population, too:

Asian women and Pacific Islander women have the highest average age of first-time mothers, compared to all other races, according to CDC data. American Indian and Alaska Native women have the lowest average age of first-time mothers at 23 and 24, respectively.

When there is nothing that can be gained from others

That will always exist. If everyone has enough resources, we'll compete for other stuff like status symbols. That's just how human nature is, we're never content and always want to progress relative to those around us.

And no, human population doesn't need to go down. Every time we get to some number scientists pick for a maximum, we blow past it and figure out how to sustain the new population. I don't see any reason for that to change, we're remarkably good at solving problems we create, though frequently later than is comfortable. I don't know where you're pulling that 528 million figure from...