Do you have any source to support your claim he committed genocide?

I have become more and more convinced—and it is only a question of driving this conviction home to the English working class — that it can never do anything decisive here in England until it separates its policy with regard to Ireland most definitely from the policy of the ruling classes, until it not only makes common cause with the Irish but even takes the initiative in dissolving the Union established in 1801 and replacing it by a free federal relationship. And this must be done, not as a matter of sympathy with Ireland but as a demand made in the interests of the English proletariat. If not, the English people will remain tied to the leading-strings of the ruling classes, because it will have to join with them in a common front against Ireland. Every one of its movements in England itself is crippled by the strife with the Irish, who form a very important section of the working class in England. The primary condition of emancipation here—the overthrow of the English landed oligarchy—remains impossible because its position here cannot be stormed so long as it maintains its strongly entrenched outposts in Ireland. But, once affairs are in the hands of the Irish people itself, once it is made its own legislator and ruler, once it becomes autonomous, the abolition there of the landed aristocracy (to a large extent the same persons as the English landlords) will be infinitely easier than here, because in Ireland it is not merely a simple economic question but at the same time a national question, for the landlords there are not, like those in England, the traditional dignitaries and representatives of the nation, but its mortally hated oppressors. And not only does England’s internal social development remain crippled by her present relations with Ireland; but also her foreign policy, and in particular her policy with regard to Russia and the United States of America. —Marx, Marx to Ludwig Kugelmann In Hanover

In other words, for the British workers to liberate themselves, they must fight for the Irish workers and support them in both words and deeds. Marx advocated replacing the U.K. with a voluntary federation of nations, quite akin to the U.S.S.R.

I recommend this excellent video which refutes third-worldist narratives on the labor aristocracy.

Replacing class struggle with national struggle is not going to better our movement. Western workers are still exploited and as proletarians (which is defined by their relations to the means of production, not their income level), their class interests remains in socialism.

different states will mostly naturally move towards socialism.

No offense, but this sounds very similar to the notion of "peaceful transition to socialism" advocated by Khrushchev. Socialism is done through revolutionary violence (a universal law), not peaceful growth.

I am not being dismissive.

I feel like this question can only come from someone in the imperial core.

I am trying to understand this question as a Marxist through a Marxist lens. Marxism has the same answers to questions regardless of where you are.

As I understand it, Mao held that "3rd world states" (a term he never used), or bureaucrat-capitalist nations, must undergo a period of New Democracy.

Enterprises, such as banks, railways and airlines, whether Chinese-owned or foreign-owned, which are either monopolistic in character or too big for private management, shall be operated and administered by the state, so that private capital cannot dominate the livelihood of the people: this is the main principle of the regulation of capital. —Mao Zedong, On New Democracy

Where did Mao Zedong state that to build socialism, a country should mass-export private capital abroad?

What source do you have that a majority of China's economy is publicly-owned? The estimates I've heard suggest that it is more like 60-80% privately-owned.

The end of this war is always one offensive away.