The difference between Gems and Coins in Summon Heroes is that Gems are the main currency for summoning heroes and general shop purchases, while Coins are spent specifically at the Item Shop, including on Trait Rerolls.

You'd need Trait Rerolls to improve a hero's Trait after summoning it, since the Trait a hero rolls with isn't guaranteed to be the best one for that unit.

Yes, you can get Trait Rerolls without spending Robux, they're also earned by completing quests, buying them with Coins at the Item Shop, or buying them with PvP Tokens at the PvP Shop.

Yes, you keep the Gems, Coins, and Trait Rerolls included with my purchase, exactly as shown in the listing.