The GBA slot supercard line has troubles with everything. They cheaped out on memory and thus suffered slowdowns, the need for extensive speedpatching in many games, general incompatibility. If you find one on the street you can use it to do a fair bit of damage to the GBA library but I would not try to use it as my everyday GBA cart, I would sooner use almost anything else.
Hacked games... if the original game works then most hacks should also work as most GBA hacks don't really place any great demands on the system over the original game. Also it is not like the older SNES stuff and N64 stuff where you require specific PC emulators.
256Mbit games/greater than 128MBit... they are not generally a problem beyond being GBA games in general. The space is there, it is just not good.
Saves. I can't remember the full setup it used. Within the game it should be as normal (play a game, save, go back to the game's main menu and do some minigames or something and then continue the adventure after that and it should be OK) but to actually save so you can turn the power off takes more effort. Said effort usually involves getting back to the menu of the supercard and then manually forcing it to write the save back to the SD. Older GBA flash carts do it automatically, newer ones will do it automatically next boot. Along with the incompatibility issues mentioned above this is what really sinks the supercard for most people. At the time it was quite cheap, had external memory when that was rarer (many were still using NOR based carts too which did not go over 128 megabytes, most were 64 or 32) and when the DS came along they were quite good at DS games (there was not a lot in it during the GBA slot era but they were the best, were fast to update and updated when many others had stopped). As they were so awful at GBA then nobody wanted them and that is why you can sometimes still find them today.
There used to be a nice compatibility list for the GBA supercards, you can still see some of it
https://web.archive.org/web/20081015031903/http://rothmans.joskeonline.com:80/supercardsite/
The incompatibility/trouble list of every other GBA flash cart that was not a supercard clone pretty much amounts to
http://gbatemp.net/threads/buying-a-gba-flash-cart-in-2013.341203/page-18#post-4756995
