Thanks for following the posting guidelines -- good job, and welcome!
Since this is a commercial product, I find it surprising that the IPB team doesn't respond to your inquiries.
I agree that the "joins without indexes" is a problem -- you should turn on the slow query log, and in particular, see this regarding index usage.
As for temporary tables, that can simply be the result of ORDER / GROUP by clauses that don't use covering indexes -- quite common indeed.
As for fragmentation, how often are you DELETE-ing records?