Lullaby Earth Breeze 2- Stage Crib Mattress - White

Does this mattress come with the mattress cover that is show in the picture?

Do standard crib sheets fit this mattress without sliding off or compromising baby safety?

If the breathability feature is in the cover and not the mattress would it just work to buy the cover and put on a different mattress?

Is the mattress itself breathable or is it just the cover?