Use "wanna" ONLY in everyday/informal speech. You're not likely to find it (or should try to avoid it) in anything formal (a business letter or email, on your resume, in a job interview, whatever)
That said, "I wanna try the ice cream" is pretty common
"She wanna try the ice cream" sounds weird
As a question, "You wanna come with me?" or "Does she wanna come with us?" sound pretty common
"I'm gonna go to the beach on Sunday" and "She's gonna go to the beach on Sunday" both sound "OK" to me (again, as a question of everyday/informal speech)
Or this one: "You're gonna wanna try the new flavor of ice cream. It's sooo good!"