A component with a size mod above 1 will require more space on larger hulls.

So, for example, a size mod of 2 would take up 1 space slot on a tiny or small hull - but it would take 2 space slots on a medium hull and 3 on a large hull.

As the hull size increases, so does the space requirement.

Not exactly. It's a percentile increase, as far as I can recall. Sizemod of 5 means the object's size is further modified by 5% of the ship's room, before miniaturization.

Yep.

If the engine supports it, yes. But it might just drop the negative. I've never tried it.