Lightsworn ruling help?? 10 points to most definitive answer?

Yes you can summon the monster that you discarded by Lumina's effect because the card would be in your graveyard already when it came to special summoning it. And for the Beckoning Light question, it would be the same exact answer. The cards you discarded to activate Beckoning Light can be added back to your hand because they were already in the graveyard.