Moogle Cards (the ones with 3D rendered Moogles) are indeed only used for EXP. They're worth more EXP than a card of an equivalent rarity. You can get whole bundles in exchange for Moogle Points by pressing the button with the orb on the bottom of the screen and going to the last tab.
Confusingly, the SR+ level
illustrated Moogles are different, and serve a role in the Ultimate Card system. You won't need to worry about that for the minute.
Yen Sids "limit cut" a card of equivalent rarity, more-or-less the same as using a duplicate card. So you use an R+ Yen Sid on an R+ card, and you'll be able to level it an additional 5 times, and if you limit cut a card enough, it will become "High Purity" and get a huge stat upgrade. Kazr discusses Limit Cutting and High Purity in this part of the
Beginner's Guide.
Fairy Godmothers boost a card by whatever number is on the FGM card, for a week. R+ cards boost the card's stats by 1.5x, SR cards by 2x, SR+ cards by 3x. You can't boost a card that's already been boosted, and some cards come pre-boosted fore the duration of an event. R+ Fairy Godmothers are fair for everyday use, though of course you want to make sure it's a card you're going to keep!
The Maleficent is okay for what it is, though it's best to work on whatever cards you can find duplicates of, so that you can limit cut them, high purify them, and work from there. You'll find plenty of dupes during the story. If you
have duplicates of the Maleficent card, great!