1) Was Keith Courage ever released with an airbox? I assume it was never sold in retail outlets since it was the pack-in, but I can't for the life of me remember if it had a box or not.
Nope, I don't believe it ever had a box. Good catch.
2) Did any PC-Engine games have airboxes or anything notweworthy besides the jewel case and spinecard?
Some of 'em came in a box when packaged with other goodies, such as
Forgotten Worlds packed with a Avenue Pad 3,
3x3 Eyes packed with a VHS tape, and surely a few others. Besides these few titles, hundreds of other games came with posters, stickers, or other fun stuff folded up inside the jewel case (also true of some US releases).