For the stars, Try taking him out for dates, or hang out with him, or simply call him during the night. And for the costumes, Once the ability to go outside is unlocked (Your popularity must be Known or Higher) , head to the Love Hotel and you'll see a option to buy the costumes ^^
P.S.: Seems like you can buy some Sexy Costumes from the guy in the park with the sign? I'll add it in here in case you're looking for that instead ^^ (To get him to talk to you, Your knowledge must be Genius ^^)