Dallas Stars general manager Jim Nill is the first to say running a pro hockey team is a day-to-day, year-round operation, so naturally there are a few things to be tidied up before the Stars hit the ice again next fall.Coming off their first playoff appearance in six seasons, here are five off-season storylines for the Dallas Stars:When or will Rich Peverley play again?After suffering a cardiac event toward the end of the season, there are questions about when or if Rich Peverley will return. He has another year on his contract with the Stars before becoming an unrestricted free agent. On Tuesday, Peverley said he is still many tests away from knowing whether a return to the Stars or even to hockey is in his future. So far, he hasn’t participated in any workouts that would raise his heart rate as he recovers, but he will need to undergo more strenuous workouts under the supervision of doctors later this summer. Will the Stars pursue a No. 1 defenseman?When asked, both coach Lindy Ruff and general manager Jim Nill said on top of their wish list is a No. 1 defenseman to headline the team’s blue line. But the need is unlikely to be addressed through free agency. That leaves Nill with one of two options: putting together a package of players to trade for that ever-elusive No. 1 defenseman; or draft and develop that player, the latter of which is not a quick fix. The Stars’ prized prospect at the moment is a Swedish defenseman named John Klingberg, who could make a push onto the NHL roster next season.Does the team need a new backup goalie?Tim Thomas is an unrestricted free agent and is unlikely to return to the Stars. This leaves room for one of the Stars’ two AHL goalies, Jack Campbell and Cristopher Nilstorp, to step into the role as Kari Lehtonen’s understudy next season. Nilstorp saw action in five games for the Stars last season, posting a 1-3 record, an .897 save percentage and a 3.09 goals-against average. In Cedar Park, Nilstorp saw the most action this regular season, recording a .918 save percentage with a 2.45 GAA in 45 games played.Will the Stars keep the core players together?The Stars don’t have many players rolling off contracts this off-season, leaving few real decisions to be made. Ray Whitney and Vernon Fiddler will become unrestricted free agents and might have a chance to re-sign with the club. Fiddler is the more likely of the two. The Stars also have a handful of restricted free agents whom Nill will work to sign in the near future, including Antoine Roussel, Cody Eakin, Brenden Dillon and Dustin Jeffrey. On Tuesday, Roussel said he hopes to play out his career in Dallas.The next NHL coach?Nill said the mark of a good organization is when other teams call to request interviews with assistants and minor league coaches. High on a lot of teams’ lists might be Texas Stars head coach Willie Desjardins, who was the AHL’s coach of the year last season after taking Texas to a South Division regular-season championship and earning a No. 1 seed in the Western Conference in his first year at the helm. This season he led the Texas Stars to another No. 1 seed in the Western Conference. Desjardins might grab an NHL coaching gig as opportunities open in the off-season.