Is it ok to use "בשביל" instead of "ל"?
Can't you omit the subject pronoun here(leave out הם)?
Not exactly. If you omit the הם it will sound like you really don't care who will pray as long as somebody will do it. I would translate "אני בטוחה שיתפללו לתוצאה טובה" as "I'm sure there will be prayers for a good result."