Slats
I fly Lear 60's, so this hits pretty close to home. No they do not have slats. Flaps are normally set to 20 degrees for takeoff, so they should be visible.
Flaps are only set to 8 degrees for takeoff when departing from mountainous airports, when a higher climb gradient is required.
The takeoff warning horn will sound when thrust levers are advanced past 80% and the flaps are not set at either 8 degrees or 20 degrees (i.e. up or down).
Sparks would indicate, to me, that something was dragging from the aircraft, what this might be, I don't have an idea.
If the takeoff warning horn was sounding, "and" they continued the takeoff, at rotation, they may have put the tail on the ground, and had some sparks from that. If anyone can get a good look at the delta fins to see if there are any drag marks, or if they are worn down, that might help provide some insight.