About picking up the weapon:
Firstly, a minigun is a very heavy weapon. It's not easy to lift and it's not easy to move around at speed. That's time you're spending not watching for Aliens and it could be fatal. Not to mention that you'd have to take the ammo pack, too, otherwise you'd be locked in place. Unbuckling that from the corpse and putting on yourself is even more time spent vulnerable. Once Blane/Blain goes down, it isn't worth trying to use the minigun.
Grenade launchers are probably fairly effective against Aliens (but then again, they've taken worse and come away without a scratch, so who knows?). And even assuming that regular, non explosive gun rounds would do any damage, they're likely to be eaten up in the Alien's acid blood before they bounce around or penetrate deeply. As per the first AvP film, A:R and Alien, that would is probably going to heal really quickly. There's every chance that a significant portion of them will just bounce off, though, as per the handgun rounds seen in the movie (which are larger than rifle rounds).
The general forum consensus is that AvPR doesn't count. And that's a good consensus. It can't count. It simply contradicts too much of what's already established by previous films to make any sense. I won't pretend that I want it to count, but anyone can see that it just doesn't reconcile with what's presented in the other films. How can something be counted when it flatly contradicts the source material for no reason? Rhetorical; it can't.