Thanks to Rick Katz for raising some good questions.
Regarding his third question about whether visiting Yasukuni will hurt regional cooperation vis-a-vis North Korea, a friend on Facebook reposted a message from Abe's Facebook page that was supposedly authored by his Secretary. There DPJ Upper House member Tokunaga Eri is quoted as saying during Upper House Budget Committee deliberations that the Yasukuni visits by several cabinet members had worsened relations with China and the ROK, and this is discouraging for the families of those abducted by North Korea. In reply the State Security and Disaster Management Minister Keiji Furuya snaps "Who said anything about getting discouraged?"
Then Abe's "secretary" accuses Tokunaga of weakening Japanese diplomacy with this remark. Then in follow-up comments Abe or his "secretary" accuses Tokunaga of "lying" and says he will not allow the abductee victims to be "used" in this way. In another subsequent post he claims this quote indicates that the DPJ is becoming like Shamintou (shamintouka), which is points out is a "comrade party" of the North Korean Worker's Party.

I don't follow Abe's Facebook feed regularly so this may simply be par for course. Nonetheless, I get the impression that Abe is hitting back hard because he fears that Tokunaga's point could damage his administration's foreign-policy image (and maybe even because he thinks to some degree she's right).
Although Tokunaga's point about the abductee families becoming "discouraged" is probably wrong in the narrow sense given that they have tended to align with very conservative if not right-wing forces, she is obviously spot-on that the visit to Yasukuni, by damaging relations with Korea and China, is a set-back to efforts to coordinate pressure and diplomacy towards North Korea on the abductee issue, not to mention the nuclear and other issues. The reputation the Abe administration has as being hawkish, right-wing, and hostile toward Asian neighbors, has the potential to become a real vulnerability with the public moving forward, just as the DPJ's reputation for being hostile to the US alliance and pursuing a weak diplomacy did real damage to its political brand.

Best,

Paul Midford