Well, I guest it's high time for some update. I've found one c64 on which my card is not working but the fault could be on this certain machine side. I found out - thanks to Jens for tips - that you have to be very careful when pressing reset/freeze buttons and try not to bend the card during this operation. This helps a lot and freeze is stable when properly pressed.
Now I still need to find out why MMC Broweser is not working. Also it seems that there is no way to connect REU to MMC Replay
This could be problematic for those who used RR to code on real thing (especially when using TMP) , I could live without REU if MMC Replay would keep memory of RR after reset - on RR after reset I still could access my sources from TASM. This is not longer possible in case of MMC Replay I believe...
Many thanks must go to tnt/beyond force for helping me sorting out MMC Browser issue.