2000 Ford F-250

Let me try to pull up some wiring diagrams and I'll post back.

Sounds like a wiring issue or more. You may need to check for a draw, the procedure is on bottom. I think a DVOM set at milliamps is the best way of measuring instead of a test light.
https://www.2carpros.com/first_things/why_is_my_car_battery_dead_over_night.htm

Let's treat these as separate problems.

On the horn. Put power and ground directly to the horn itself and see if it works.

On the dome light. Switches are pretty common on these and worse yet new have been found to be defective. What I would do Is get some thin lubricant like wd-40 and spray the latches thoroughly and open and close the doors 20 times or so to work the latch. That may take care of the dome light problem, but if it doesn't a scanner will be needed to work the door ajar switches to determine the bad one.

On the Blower motor. I think two problems may exist on this. One the resistor is likley bad. The high speed goes separate from the resistor. The resistor just modifies the electrical output to the motor to slow the motor speed down.

On the battery drain or draw. Since the blower stays on high with the ignition switch off, this is probably the circuit that has the draw.

I am going to get you diagrams and send them to your email.

Did the horn work when powered up?

Did you spray the latches?

Look at the diagram I sent on the blower motor. See how the power goes through to the resistor and these are the speeds you are having a problem with? Replace the resistor if the connections look good. Do the other speeds now work?

Did you check for which circuit the draw is on using the link I sent and the diagrams I sent? Or is the draw on a different circuit?