Any question answered...

@OmarLittle - the Miche BB requires the Campag tool so your Shimano one won't fit.

As for the axle length, I think Miche only do a 107 mm axle length so I think it's safe to assume that's what you'll need to replace it. Be careful when buying a new one as you'll need an BB with ISO taper and not a JIS one (which rules out most Shimano ones).

Ah, that old chestnut. Ask around, I think people are happily using Shimano BB-UN54 107mm JIS with Miche cranks. The suspicion is that when Miche changed their spec from 110mm to 107mm, it was simply to accommodate a change of axle supplier from European made ISO axles to Far Eastern made JIS axles