The second item - State - I agree with Marx.
The third item - Religion - perhaps Marx was influenced by the European Renaissance which seeked to remove the oppressive and corrupting things from the then European understanding of Christianity. He should have reflected that some past religions, or at least their originators and preachers, spoke about social, economic and political justice and advancement. For example Prophet Jesus preached against the wrongs done by the traditional money lenders and then Prophet Muhammad created an entire set of progressive socio-economic laws. Just yesterday I spoke of Communism and Religion in this post of mine, a reply to another member.
But then in a Marxian perspective, Jesus (a.s.) did not found a religion but was a social revolutionary whose struggle was ultimately aimed at the abolishment of the state, money and yes, religion too. The distinction between sacred and profane, which is a component of theistic theology, conflicts with Marxian thinking, to which everything is sacral.
1. Did he really say "no more schools and universities" ?
To Marx, all knowledge is intrinsically ingrained in every person. Thus the very act of compartmentalizing, subdividing knowledge and intelligence into separate disciplines and then dispensing it in the framework of an "education system", is another superstructure of the capital and designed to organize society according to the needs of capital. Where future workers get alienated and prepared for a life of being exploited.
In that sense, schools, universities and any other centers of institutionalized learning of the expertises of the capital are something Marx would definitely include among the attributes of capital, which are destined to be wiped out by the radical proletarian revolution.
3. About "no more money" I don't know if money can be abolished despite technological advancements like 3D Printing but I have proposed an economic system in this thread which ensures that there is no economic disparity, no economic classes. Please do read the OP and the subsequent discussion and leave your comments there.
In communism, there certainly can be no money. No price tags, no property, no purchasing nor selling anything. Not even barter trade.
Well, I myself purchased his Capital some years ago from a secondhand bookshop. IIRC it had two thick volumes. I expected it to have philosophy but when I open them all I saw were numbers so stopped reading them.
I confess that I too am far from having read it in its entirety, confining myself to select excerpts.
However, and this will be the most important part of the present post, I was lucky to discover a contemporary author from France who not only spent his time reading practically everything Marx published all day long for numerous years, but whose understanding and reading of Marx and thus of what communism means is simply extraordinary. His lectures and commentaries surely represent one of the intellectually most stimulating things I came across during the past couple of decades.
Now unfortunately there's almost nothing by him in English (and I'm not sure if you understand French). Still one English-subtitled video of a conference he held is luckily to be found online.
So I'm glad to be able to share with you this hour of amazingly insightful and instructive deliberation about Marx and communism. The level of acumen is simply mind-blowing.