I would check your specific airline to be sure but I have never had an issue of taking my stick on an Airplane.
Yes, Lacrosse Balls are hard & made from solid rubber.
I occasionally wash my lacrosse gloves in the washing machine but not frequently. If you have leather palms I would stay away from Machine Washing but once a year is fine. Toss them in a pillow case to be safe and air dry.
A lacrosse ball is not hollow rather than solid rubber.