There are many mistakes in the paper. The answer to the question whether the proof is correct is therefore negative; it is not correct. A correct proof does not contain several mistakes.

But still, assuming that it is possible to get a rough understanding of the idea, we can consider how much sense it makes.

The conjecture, as it is generally understood, suggests that every even number greater than 2 is a sum of two primes. The paper instead considers the version in which every even number greater than 4 is required to be expressed as a sum of two odd primes. The conjecture applies to all even numbers from 6 and higher. 

If the idea of the proof is correct, it should show for every even number \(N\) greater than or equal to 6 that there are two odd primes \(p,q\) with \(p+q=N.\) If it does not do this, then the idea is not correct. Do you see how the proof shows for \(N=6\) that the primes \(p\) and \(q\) exist? More precisely, in expression [9], what are the values of \(p_1,p_2,p_3,p_4,p_5,p_6\) that make the proof work in this case? 

Thanks for putting it so clearly and succinctly. +1