Who has used the bassinets on international flights?

We're flying to europe in a couple of weeks, with DD who is 5 months old. I'm not sure what we need to take to put her to sleep in the bassinet on the plane.

Did you have trouble getting a bassinet after requesting one? I have no idea whether they overbook them or not?

Does the bassinet have a mattress in it that I can tuck a bunny rug around? Or do we need to bring something to be soft underneath?

Does it have some kind of harness so that DD won't go flying if there's turbulence? I got a baby b'air for when she's awake on our knee, but that won't be so good when she's sleeping in the bassinet.

Thanks!