>>24
The rate can be seen as a colored circle next to the character when you are choosing which one you want in your party, it goes from red, to blue, to pink to gold... I think, the more it increases small circles start rotating around the big one.
The card is given you when you beat the game, just like that.
She is an special character recruitable only after beating the main story, so there is no actual "relation" developed between her and Haseo, she actually mentions how jelly she is that Pyros got to save Za warudo twice.
She actually has an ending similar to Azure Kite/Balmung/Orca