Blackbird,
Q1. Your wife can visit any time during your training and there is no need to leave Japan. Bear in mind, though, that you are going to be busy, so most people wait until they are in the simulator part of the training (or OJT) when you will have a schedule and, therefore, a better idea of when you will have time to go off and do things together. There is no time specifically given off during your training for your wife to visit; you just have to fit in around the Company's requirements. The only time NORMALLY scheduled off will be between your ATPL sim check and the startof your OJT. This is NORMALLY 10 days and the Company will pay for your return ticket in order that you can go home during this period. Sometimes delays occur when, for instance, JCAB can't do your sim check or Christmas time reduces the flying program. In this case there may be the opportunity to have some more time off but it is definitely not par for the course and should not be anticipated, nor planned on, in order to organise visits. Back to your question though; you will be expected to remain in Japan during your wife's visit, as you'll be in training and you will have to squeeze things in around the sims etc (which actually isn't as difficult as it might sound as you ofetn have 1 or 2 days between sims).
Q2. There is virtually no movement in AJV and I believe that is the same in AJX. AJV is still expanding and ANA is keen to take advantage of the extra runway being built at HND and the increase in international traffic at NRT. In order to do this they need to be able to jump in when slots etc are offered, hence the requirement to have more pilots (and aircraft). AJV's original plan was/is to have 11 aircraft and we now have 7. We just about have enough pilots to crew the operation and the merger next year with AJX MAY reduce the requirement to recruit some pilots but this is certainly way above my pay grade and purely speculation on my part. The Japanese still have a huge pilot retirement 'bulge' and they need to get pilots from outside the country. Of course, things could get interesting with JAL and their lack of financial success but, for the time being, ANA in the guise of AJV and AJX still needs additional pilots, not replacements.
Saveconcorde,
Your snipey comments aside, you are now armed with the information you sought, regarding hotel versus apartment and the financial aspects of having your wife stay longer than 2 weeks, so hopefully your question has been answered and you're better able to make your decision.