Re: If indeed some type of joined-primes does stop at some point, why would it?
Here is a link to a pdf version of his article. Prima facie I would wager that there are infinitely many twin primes, because if at some point they would start exhibiting differences always larger than two that would make some sort of regularity in the sense of a non-probabilistic divergence plausible, while so far the primes have proven to be as unpredictable as possible. I have to admit, though, that I am not too familiar with number theory and have yet to read that article by Zhang in full to make any properly founded statement.
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