We've never been really sure what happens as an individual is assimilated and becomes a drone. Complicating the issue is the change in the Borg from before and after First Contact - so that's how I'm going to tackle it. Then, I'll turn to what Voyager has shown us about recovering from Borg control; anyone who's seen "Survival Instinct," please feel free to contribute.

Before FC

Only one assimilation is seen, that of Locutus. Picard's uniform is removed and replaced by the neoprene suit, and various implements are surgically grafted to his body. Even after assimilation, the process continues: a probe turns his skin a grey colour, and a manipulation tool is placed OVER his hand - it does not replace it, presumably because otherwise Picard would spend the rest of the series with a bionic arm as well as heart. And to my mind it's a major error. It doesn't make sense to just slip it over the existing limb.

When Hugh is separated form the Collective, no attempt is even made to remove the implants.

After FC

Assimilatees are injected with nanoprobes, causing immediate skin mottling (the 'new' Borg have an idfentifiably alien/zombie skin colour) and spontaneous growth of implants. Neural control is not established instantly: the victim is conscious for the first few seconds.

It's what happens next that causes problems. New drones are seen being given optical implants (fitted onto extrusions which either grew or were inserted into the eye. . . lovely) and tools, the latter which appear to REPLACE limbs which have been removed. But the major problem is the suit. This appears to be some sort of armour, but is it grown or worn? Why does Ensign Lynch have his uniform underneath? Why does a Starfleet drone - who appears to be Ensign Paul whatsisname, one of the first assimilated - continue to have hair and a uniform long after others such as Lynch and the Bolian are fully converted?

There's also the matter of Lt. Hawk. Why is he taken elsewhere for assimilation? And is the fact that he's unable to deflect Worf's phaser significant?

Recovery

Picard was able to have all internal and external implants removed. Conveniently neither eyes nor limbs were interfered with while under Borg control. However, in FC he remains able to sense the Collective's consciousness, and dreams of the spontaneous growth of implants (which we know happens) even though such an incident was never seen to affect him (that we know of; maybe he did once sprout transistors at the drop of a hat).

Seven of Nine is more interesting. As I understand it, both her eye and left arm are bionic, and hair growth has been stimulated. She still has nanoprobes in her system, which occasionally get restive, and can even re-develop the ability to deflect phaser fire. The suit she wears is meant to replace some functions of her body damaged by years of assimilation (or something; I'm not complaining!).

It also showed his right arm to be extremely pale, with the words "synthetically grown arm" written next to it, or something to that effect.

Obviously, during pre-production, anyway, the implication was that his arm was removed, and replaced or regrown thanks to 24th century medicine.

Now, the episode itself never mentions this. Then again, it never shows Picard wearing short sleeves either. I'm willing to say that his arm was indeed removed by the Borg.

Vaccum-sealed drones:

A few ideas. Their armor seals off most of their body, save for the hands and head. Perhaps the nanoprobes can seal off the exposed skin from the more destructive effects of vaccum? The same would go for the eyes.

But I do have an answer for the "hearing" of the collective. I don't think that in BOBW we ever got a line saying that 'all' of the implants placed in Picard were removed, and both Picard in FC and Seven at some point have mentioned the Borg neural processor installed in every drone and without which they would die. It seems likely to me that this was left in Picard because it was basically a shunt in his spinal cord which, while not active in terms of transmitting, was still active enough to trigger the subconscious use of typical Borg neuropatterns in his brain, manifesting as nightmares.

As far as the Hugh problem, that was the first instance of a Borg separated from the collective but still a drone, technically. Possibly they didn't know enough about removing the implants? Or more likely, the idea was discussed in some meeting to which we were not privy, and overruled in favor of using him as a tool for destroying the collective. When they decided against that plan perhaps it was too late to try and 'fix' him.

The hair, skin mottling, etc I usually just chalk up to the bumpy forehead-Klingon thing. It's just the makeup. Though I do actually have a rather long theory on the bumpy foreheads involving Klingon geo-politics, etc.