I'm of the personal view that an engine does not turn a car into a death trap. People turn their car into one. Often, it is through neglect; by choosing to not upgrade or refurbish or revisit worn-out essentials like brakes and suspension, when they bung in a swanky new engine. Other times, it is by driving irresponsibly; endangering their lives, as well as those of others. So let me state: the 2JZ-GE (or GTE, for that matter) is NOT a death trap per se, on its own.
Regarding the 2JZ-GE engine, it's a good powerplant which is smooth, offers good power, torque, and is reliable. In essence, though, it IS a 'car' engine at the end of the day...whose best application is for medium to large sedans.
In off-roaders and SUVs, there is more of a requirement for lower-revving engines, which deliver peak power and torque at significantly lower revs. Since you're planning to use it in an FJ40, you probably have some reason why you want to replace a low-revving engine with a higher revving one. You probably also have a specific reason why you're choosing it over a 1FZ-FE (petrol) or a 1HZ (diesel) or a 1KZ (diesel); which are all better suited to SUVs.
To answer your questions, to the best of my personal knowledge...
Anywhere between 60-85K is about the going price for a 2JZ-GE. This depends on the condition and vintage of the engine and should include the transmission, airflow, wiring, and ECU etc. A lot of 2JZs are advertised as "Kabli" but are actually, rejects from cars that have been fitted with other engines. Careful scrutiny of this aspect is warranted.
It's a 3000 cc engine, which you'll be using to drive a Land Cruiser. You'd be lucky to get 8-9 kmpl.
You don't NEED to change the differentials, in the sense that it's not a must. You might want to consider this aspect that the 2JZ (mostly used in Crowns and other large sedans), drives a very different sort of diff, from the heavy, immensely-robust FJ40 one. Most people choose to swap diffs too, so as to upgrade them, at the time of engine swap. 60 or 80 series Land Cruiser diffs, and Nissan Patrol diffs are popular choices, in this regard.
In essence, pretty much any engine can be coupled to any transmission. A lot of people have already done this, in some CJs. I've also heard news about this swap (2JZ with manual tranny) being performed in a Hilux, although I have no real evidence of this.
If you have any further specific questions, feel free to ask. Best of luck.