Who cares whether it is or isn't sanctioned; what it tells me is that Pakistani's would be marrying their cousins even without Islam; it is a practice that pre-dates Islam.
As for encouraging, it never does - there are numerous hadiths that talk about that it is best to marry outside the tribe to build up a larger web of interdependent and thus make the 'collective' stronger. Muhammad might have been a 7th century war lord but he wasn't dumb when it came to the benefits of marriage across tribes and between different peoples.
That's long been understood as being a way of developing strong ties with other groups and tribes. Hence why even European royal families all married into each other.
The Book of Common Prayer has almost exactly the same rules about who you can and cannot marry as Islam, but Anglicans almost universally do not marry cousins. I think cousin marriages are more of a cultural thing which is backed up by Islam. I wouldn't say Islam specifically encourages it; more it allows it.
Yes, but of course, Islam is itself something that's heavily influenced by the culture of 7th century Arabia. Religion and culture are inextricable.
The only thing is, it's slightly odd for the so-called perfect religion, which is the solution to all human problems, to permit such a potentially harmful practice as inbreeding among a family. I would imagine that Allah, being omniscient, would have known the dangers of such cultural practices and would have subsequently banned it outright, rather than giving it direct sanction in the Qur'an (33:50).
It's particularly ironic as Islam strictly prohibits things which are comparatively quite harmless, like chess or eating pork.