Your opponent cannot activate "Appropriate" after you activate "Graceful Charity" since the last effect that resolves with "Graceful Charity" is discarding, not drawing, and your opponent misses the timing. But if your opponent already has an active "Appropriate" face-up on the field, he/she can draw 2 cards after you activate "Graceful Charity".
If "Solemn Wishes" is on the field when you activate "Graceful Charity", you gain 500 Life Points after you finish both drawing and discarding. If "Solemn Wishes" and "Skull Invitation" are on the field, you finish both drawing and discarding for the effect of "Graceful Charity" then you gain 500 Life Points, then you lose 600 Life Points.
If you have three pieces of Exodia in your hand, "Graceful Charity", and no other cards, and then you activate "Graceful Charity" and draw the final 2 pieces of Exodia, you must discard 2 cards before a victory can be declared, but after you discard you will no longer have all 5 pieces of Exodia, and cannot declare a victory.
Spell|
Normal
Limited