The anime has just finished vol 2 (Raven's Nest) at episode 5 and did one of vol 4's (Days in the Nest) sidestories which took place chronologically before vol 3 (Chimaira Dance). This is the current arc the manga (and anime) is in which takes place at the end of first semester.
As for what the anime would skip, I think what suffer here would probably just sidestories for the most part. Other than that assuming every other vol will animated like vol 1 (episodes 1-3) we probably shouldn't lose much beyond some dialogue and a minor scene or two. This also based the assumption that later vols like 6 aren't significantly longer than vol 1. A novel reader like versionf would have to confirm that or not.
IMO the most sensible structure the anime could do to adapt the novels comfortably enough without loosing too much is this:
- Vol 3 = episodes 7-9
- Vol 4 & 5 = episodes 10-12 (These two volumes are really one volume and vol 4 can adapted into one episode since there only a partial main story)
- Vol 6 = episodes 13-15
- Vol 7 = episodes 16-18
- Vol 8 = episodes 19-21
- Vol 9 = episodes 22-24
- Rest of the sidestories = OVAs and specials.
Miyachi hasn't been introduced yet as far as scanlations have been covered, but Dairenji Shidou was mentioned in chapter 18. He is of course Suzuka's father and the original leader of the "Two Horn Syndicate" aka the "Yakou Cult", though it is known by the "Order of Northern Star" to the public nowadays. He also worked directly for government's Imperial sector as the general manager of their "Spiritual Service Division" which was dedicated secretly researching Yakou's "Imperial Arts/Style" magic system and it's soul manipulation aspects for their own personal use. Shidou later died in a large-scale incident 2 years ago that he planned and brought about concept of "spiritual/paranormal terrorism" for the first time ever. The Two Horn Syndicate organization was then label as a terrorist group for the disaster and breaking the law on forbidden spells, thus hunted down by the Onmyo Agency.
BTW, Also stated in Ch 18 and 19 Touji was one of victims of this incident. There is no cure for the affects he suffers but he can get treatments periodically to aveilate some of the symptoms, however he has to live with it for rest of his life. Saying anymore beyond this requires a spoiler tag as the scans have not reached here yet.
Lastly, D was never the leader, this organization had no ties to him until two years ago as implied in the manga. He seems like he's more of an ally who's using them for his own purposes.
Does that help?