Not CM 11, MIUI v5, v6kk
Yes CM12.1, Mokee 51.1 (recommended), Sudamod, v6 L, v7 L
As you realize you cannot have both.
As for the MiRecovery i suggest you sMIUI, but no, there is always an option when you flash MIUI via TWRP to avoid flash recovery. (sometimes was exist i hope today too but...