Is there any proof that its really his bitcoin address?
No, but if you look at the header, you can see that it was likely an address that was mined by satoshi as the headers of blocks that he mined has somewhat of a unique 'footprint'
I don't think it is beneficial for people to be obsessing over satoshi like this, as it creates a colt like religion.
If it were up to me, satoshi would sell all his coins on an exchange. It would make the price crash over the short term, but over the long term it would benefit Bitcoin as it would take a lot of uncertainty away and would prevent a lot of what the OP is doing