Non-reflection of the bad set for \check{I}_{\theta}[\lambda] and pcf

We reconsider here the following related pcf questions and make some advances: (Q1) concerning the ideal $\check{I}_{\kappa}\lambda]$ how much reflection do we have for the bad set $S^{{\mathrm {bd}}}_{\lambda,\kappa} \subseteqq \{{\delta < \lambda} : {\mathop {\rm cf}\nolimits \, (\delta) = \kappa}\}$ assuming it is well defined (for transparency only)? (Q2) are there somewhat free black boxes? The advances in (Q2) will be used in subsequent for constructions of Abelian groups and modules.