Does Komeito do well among Burakamin?
Burakumin are actually an interest group for Heisei Kenkyūkai, one of the relatively moderate LDP factions. Komeito probably does okay with them as well, but not as well as it might otherwise.
Regarding the questions about the JCP, it is no longer classically "commie" but is still focused on material issues. Shii Kazuo waving around a rainbow flag or talking about Japan somehow needing more abortion of all things would come across as transparently absurd to just about everyone (although my understanding is the JCP does
support LGBT rights). Policy-wise they're basically old-ish-school social democrats right now.