No, Communism per Karl Marx's Communist Manifesto, which I listed in the OP before the - mark, is NOT what the early Christians practiced. To say it was is to push Marxist propaganda. Communists that work against Christ exist within today's Christian Church also, even as KGB defectors have warned (Golitsyn for one who was a KGB colonel that defected to U.S. in the 1960s).
A record of an early Christian community exists for Jamestown, with Christians that settled there basically in the wilderness. They learned early on that keeping everything in common did not work, for many starved. From 1609 to 1610 many starved because there was no INCENTIVE to work to produce it.
That's an example of what happens when everyone knows they will receive the same, whether you work or not. Economically it does not work! That has been one of the biggest problems in Communist countries, they have to try and police those who don't work, which is really impossible to truly do in a large country. It means you wind up with a lot of atrocities just to try and get everyone to work.
Yet the Bible way, God's Way, like Apostle Paul said, if a man won't work neither should he eat (2 Thessalonians 3:10).
The settlers at Jamestown the next year applied that Bible principle. If you didn't work, you didn't eat. What you produced you got to keep and trade or sell any extra. That next year no one starved, and there was abundance. THAT... is the 'free market' or 'free enterprise' system! It works, because God created it.
So let's settle the matter about things in common per Apostle Paul...
Paul Teaching To Do Alms, Which is Not By Commandment:
2 Cor 8:7-15
7 Therefore, as ye abound in every thing, in faith, and utterance, and knowledge, and in all diligence, and in your love to us, see that ye abound in this grace also.
8 I speak not by commandment, but by occasion of the forwardness of others, and to prove the sincerity of your love.
9 For ye know the grace of our Lord Jesus Christ, that, though He was rich, yet for your sakes He became poor, that ye through His poverty might be rich.
10 And herein I give my advice: for this is expedient for you, who have begun before, not only to do, but also to be forward a year ago.
11 Now therefore perform the doing of it; that as there was a readiness to will, so there may be a performance also out of that which ye have.
12 For if there be first a willing mind, it is accepted according to that a man hath, and not according to that he hath not.
13 For I mean not that other men be eased, and ye burdened:
14 But by an equality, that now at this time your abundance may be a supply for their want, that their abundance also may be a supply for your want: that there may be equality:
15 As it is written, 'He that had gathered much had nothing over; and he that had gathered little had no lack.'
KJV
2 Cor 9:7
7 Every man according as he purposeth in his heart, so let him give; not grudgingly, or of necessity: for God loveth a cheerful giver.
KJV
What Paul is describing is doing Alms for other brethren that are needy, and to do it not by command, but via the heart and compassion for them, and not to do it so much that it puts a burden on yourself. This all Churches in Christ and its members still do today.
But under the system of Communism, what happens? The State takes... your abundance and more so that you become one of the needy, because that is a principle that Communist systems use to keep control of the masses, i.e., keep them on the edge of starvation. But the Party, they have access to the abundance because they control it. Because of this, lack of incentive to work was the result, which made economic conditions even worse!
It makes sense that if the State is going to take the results of your labor away from you and just give you what 'they' think you need, that you won't have much incentive to really produce. Thus since Communism started, those economic systems have had to have economic help from the free enterprise systems in the Christian West. Only when Communist countries like Russia and China eased off some of their Marxist principles over the people, and freed up enterprise somewhat in their countries, has their economies gotten established. So all that was about was their finally recognizing that Communism does not work economically, but God's Way does, whether they want to recognize God's principles or not.