Rule #1 - assume nothing.
The steering on a Jimny has four "ends" any, or all, of which can be worn, and can cause play, as can the king pin & wheel bearings - you need to determine where the problem lies as the first step to fixing it.
1 - Can the box be rebuilt - consider the answer to be no - if it is worn you're going ro have to replace it.
2 - Prices where you are, are different to prices where I am, if you're lucky an Australian member may be able to answer the question, but you're more likely to get it answered if you ask it on an Australian forum - try auszookers.com.
3 - Yes - if the wrecker will sell it - but ask yourself - is it likely to be in any better condition than the one you have?
4 - Both - the steering box has internals that are a part of the power steering - but - there are also other parts that are external - pump, lines, etc.
5 - How can we answer this question when we know nothing about you - is it something you can do?
Power steering can be added, and whilst I've never done it, it's my understanding that it is not difficult to do - you can either swap in the pieces from a Jimny with power steering, or you can adapt the bits from a Vitara.
Based on your questions, I'd say you are not just a novice to forums, but also to the world of motor vehicle maintenance & repairs - there's nothing wrong with that, we all had to start somewhere, but, certain aspects of vehicle maintenance are critical to continued good health, steering, suspension & brakes fall into that category, and it's best that you gain the experience at the side of someone who has it - pay a visit to the auszooker forum, there may be a member who lives close to you and can assist you.
Oh - one last thing - welcome