Is every number $2p$ , $p>3$ prime , the sum of two DISTINCT primes ?
The case $n=2p$ is no counter-example of the Goldbach-conjecture because $n=p+p$ shows that $n$ is the sum of two primes. For $p=2$ and $p=3$, the only partitions are $4=2+2$ and $6=3+3$, but $10=3+7$ , $14=3+11$ , $22=3+19$
Is it known whether there is always a solution with distinct primes ?
It is not known, but it is probably true. Note that PNT heuristically tell us that, if we call $r_{2}\left(n\right)$ the number of representations of $n$ as a sum of two primes, we have $$r_{2}\left(n\right)\approx\frac{n}{\log^{2}\left(n\right)}$$ hence, the number of representations grows if $n$ grows.