Are there ever field goal attempts on first down?

Answer 1

Not unless it's at the end of the game or first half, with little time or no timeouts. (In the NFL, a free kick after a fair-caught punt or kickoff is technically an untimed down.)

When wind is a factor, it could come at the end of the first or third quarter if a team badly needs points and has been struggling offensively. Changing sides on the field could make a kick difficult against the wind.

Field goals are often attempted to either go ahead at halftime or win the game at the conclusion, and they can come on first down. But if there is any time at all, or a timeout available, most teams will try to improve their position on first down, and if necessary try a kick on a later down.