More 'just came back' questions (soul weapons ...)

You get the emblem for your DrK by doing the Maple Island quest line. If you don't have a lightbulb over your head, check your Adventurer Book ("Episode" in key settings) to see how far you've gotten in that.

There is no way to get any more Hot Summer Coins. The shop is only open for people who for some reason didn't use all they had while the events were still going.