Unfortunately, Spiritual weapon has only the shape of a weapon, not the statistics. So the spiritual weapon does not get properties like Heavy, To reachetc. It just looks like the weapon you choose. (Note that the damage cubes are also independent of the original weapon.)
Depends on whether you and your DM see at eye level how the phrase "for one of these weapons (eg, weapon focus)" is interpreted. This can mean either "any heroic act that applies to any weapon from the preferred list" (your version) or "any heroic act that applies to a weapon (such as Weapon Focus), which is also on the preferred list."
In fact, Daisho's expertise only applies to multiple specific weapons – but not in the way the example does. Weapon Focus requires you to pick one weapon type and share that mechanic with several other tricks (such as Improved Critical or Weapon Specialization). Since Weapon Focus is mentioned as an example of a "weapon-specific" feat, the intent was probably to be able to use only those feats with this class feature. In addition, Daisho's expertise is not valid for one type of weapon, but for two types of weapons – again this might not be considered specific enough. I would say that it does not meet the requirement "meets a weapon" and therefore can not be used this way.
P.S. But the main problem this DM would have with this combo – this performance is explicitly a better version of Weapon Finesse and is only balanced by the use of Katana and Wakizashi. When used in the way you suggest, it circumvents this restriction, which makes it very overwhelming compared to weapon finesse.