- A resistive load will start flowing current according to I = E/R, and will do so indefinitely.
- An inductive load will want to keep flowing current when you break it's circuit because V = L dI/dT. When the relay opens and I wants go to zero instantly (dI/dT = -infinity) the inductor will generate enough voltage to keep the current going -- even if this means sparking across the relay contacts (snubbers reduce this, sometimes dramatically).
- A lamp is rated for its current once it is hot. When it is cold its resistance is significantly less than when it is hot; the relay needs to supply that inrush current without welding the contacts together.
- I dunno about the low-level stuff.