Just a note about the Fushigi no Dungeon 2 bug: That's a gameplay bug, not just a graphics bug. The score and floor numbers shown in the screenshot are nonsensical, and the Japanese text underneath (which sums up how the game ended) reads "Defeated by Shiren while carrying the Bizarre Box" which is similarly nonsense (Shiren is the default name of the player character, not an enemy)
The Fushigi no Dungeon games are notable for automatically saving to battery RAM after every action the player performs, so I'm inclined to suspect a SRAM mapping problem, although a CPU bug is also possible.
Probably the former, it does this:
818103 lda #$53
818105 sta $b36000
818109 lda #$54
81810b sta $b36001
MESS driver masking seems to apply at every 0x10000 (i.e. it writes at 0xb06000-0xb16000-0xb26000 and 0xb36000) ... BSNES only writes at 0xb36000 (plus it has a completely different mapped memory in there). Cart mode is 21 iirc. Ideas?