How often is this done, with the brain still being alive?
How long does it last?
It's hardly an everyday thing, but it's a level of technology available if you have wealth and connections. You'll certainly see it to various degrees within the Mechanicus, with things like their Binary cortex technologies.
In terms of longevity, it can last beyond a normal human life-time... if
the systems are high quality and well maintained - as, naturally, it involves removing the brain from many of the body's housekeeping services.
(Consider that humans are pretty low maintenance until about half a century old. In comparison, there are quite a few steam locomotives that are still working at over a century, but they needed a lot of maintenance along the way).
Also - psykers. Weaponised psyker brains. Is this a thing?
Yes. The Radical's Handbook includes the Callophean Psy-Engine. Visually, it's a little bit like a Ghostbusters proton pack - a backpack containing the sightless and terrified brains of four vivisected psykers, connected to a director wand out of which warp-lighting and witch-fire can be directed.
Alternatively, psychic null in a box.
The Culexus assassin's helmet would imply that this is probably possible, although in general the Imperium is much better with anti-psychic techniques than they are with anti-anti-psychic techniques.
They can contain and deflect psychic power pretty well, but cannot completely bottle up psychic nulls. Given the rarity of pariahs, the fact their effect couldn't be entirely contained, the increased reliance on maintenance, the higher availability of similar technologies ... it's possible, but not exactly probable.