Yeah the pre story isn't perfectly polished yet - although that's cool, rather have great gameplay and a dodgy story than the opposite
This might have been discussed to death, but it's pretty fascinating still;
The first attacks in Mumbai and Bonn showed an entirely different military paradigm - I would assume the aliens were equipped with endgame armour and weapons as well as top notch psychic powers. It wouldn't be unreasonable that they're using powerful weapons of mass destruction either. Add the fact that the ability to jam and decrypt all of our communications and we're left with not an army but groups of disconnected soldiers who don't know where anything is, don't understand the enemy and probably haven't fought in any prolonged conflict given Earth's peaceful state.
Why the aliens lose all their gear, cohesion and strategy by the time the game starts is probably some cool mystery to be worked out later. It also seems like they've never had particularly good intel about humanity's organisation. They just turned up, saw some large cities and thought "That looks like fun.". Possibly got some XVI going too, and left that to finish the job. The actual government and military weren't really threats to that goal anyway. The subsequent raids are probably just to distract humanity from the other activity.
PHALANX's personnel are the absolute elite, have communications that the aliens can't mess with and know enough about them to identify and exploit their sudden weaknesses.
I know that doesn't address everything, but those are my suggestions for now
Do bear in mind I've only played 2.4 through to the end (Looking forward to having my mind blown by 2.5 full release!).