Seems to me that for the horn, you can send a negative pulse to the OEM horn input at the OEM horn relay. You might need to swap the polarity of the alarm's signal (with a relay or onboard programming) for this.
Or just use a stand-alone relay of your own, and switch 12 volts (common and N.O. terminals on the relay you install) to the horn itself. Your call.
I'd have to look up the dome light stuff. I chose to use my own lighting for a custom thing (it's a habit from installs on BCM cars, where I don't like using the OEM circuits).
Others will have lots of help for ya.
Good luck.