TBH, I'm making a lot of this up as I go along, so keep the questions coming! The more you ask, the more I have to answer, and the more fleshed-out the world gets.
Early stages: More or less, yes. The largest cities have been destroyed and/or colonized; I'm imagining the 'first strike' was a series of kinetic impact attacks on large cities, from projectiles that then 'hatched' into attacking swarms. The nullifier effect is very EMP-like, but it's more of a persistent radius effect than a pulse - anything electrical or electronic in the field just shuts off and can't function.
Alien collaborators/sympathizers- there were quite a few of them early on in the invasion, but they disappeared pretty rapidly. The aliens don't communicate with people, but it's obvious they consider humans to be just another resource to be harvested, so the problem of people trying to assist the aliens solved itself. Captives mostly disappear into the hive complexes (yeah, I'm being lazy and going with a Bug Swarm theme), but some of them do reappear as 'thralls', humans with opaque bubble-like helmets on their heads and obviously completely under the control of the invaders - they get used as cannon fodder, living shields, and disposable scouts by alien forces.
Communications: Long-distance communication is extremely spotty. Prior to the invasion, Earth had a ton of satellites in orbit, and probably some outright orbital colonies, but they're all gone now. With the loss of the satellite networks, most communication is limited to line-of-sight or hardline setups; you might still have a portable phone, but without any relay points, it's limited in use. The internet (or whatever replaced it) is all but obliterated, since the servers and data centers were located in the cities. Television works if you can find one and are in range of a local broadcasting station - the big studios, again, were in the cities, but there's still surviving local stations in operation.
Exceptions: The field only suppresses electrical/electronic devices. This description applied to well over 90% of Earth's technology by this point, I'm thinking cheap, portable cold fusion or something similarly sci-fi, but chemical reactions and biological phenomena aren't suppressed. So an internal combustion engine or a laser rifle would be disabled, but a gunpowder weapon or a steam engine (if you could find someone who knew how to make it) still works. So your gadgeteer concept's devices would have been exempt, since they were fueled by bio-electricity; if you decide you want to pursue the android/gynoid idea instead, we can work something out.