Is it possible to pray for a friend’s conversion to Catholicism? If yes, is there a particular saint one can pray to?
Sure. As for a saint, you can pick any saint you wish. You might look at your friend’s life circumstances and choose a saint who has a particular interest or patronage in those areas (e.g., St. Joseph for a husband and father, St. Thomas Aquinas for a teacher). Some “all-purpose” saints for conversions might be St. Monica, mother of St. Augustine; and St. Jude and St. Rita of Cascia, patrons of impossible causes.