Do I need an air space between insulation and flooring in the attic?
4 inch thick insulation is thicker than a 2x4 (only 3.5" thick), which means you'll be compressing the insulation and decreasing the R value. Instead, I'd suggest laying the new insulation on top of the old (no need to throw out the old unless it's turned moldy), without a vapor barrier on the new (you only want one vapor barrier, against the ceiling), and going perpendicular (to the old to reduce the air gaps).

With 2x4 joists, I'd suggest that they are not load bearing and I'd recommend against putting any further load on top of them.