After a few weeks of use, I have to say that I've started experiencing some freezes since a few days. It first started with one freeze, then a few ones the day after then a lot in the same day. It's the kind of freezes that may be due to poor contact between the Omega cart and GBA console and it produces very weird and unpleasant distorted sounds. When you remove the cartridge during a game session, it produces the same symptom.
Of course I tried other microSD cards freshly formatted (one in FAT32/32K and the other in Ext/128K) and the same.
I sent it back to the eBay seller.
Maybe I could have tried to open it and see if I could bend the microSD pins so that it would be always touching the microSD card but I prefered to sent it back.
Not sure if I'm gonna take a new one as I guess the same thing will occur again and anyway, I so love the original cartridges, and the battery life is twice better than with the Omega.
EDIT: As it's very hard to find some games at a descent price and that are not fake (most of the games on eBay are fake) and because I want to play some homebrew, I ordered a new one. I hope I won't have any issue with it.