i have a problem with my starter engaging while its in park and in nuetral while it is running?

all started with my horn going off all by its self, started the car and the horn shut off, then i disconnected the horn( have not connected it back so dont know if it still goes off or not). after i started it i turned it off and the car kept trying to start with key in off position and out and if i put it in gear it would stop, after a couple days of driving it and keeping it in a drive gear with the e brake on when i parked it, it stopped doing it over the weekend. go out monday morning and the starter did nothing, starter was bad so replaced it. hour or so after that i was warming it up and the starter engaged? now it does it intermitantly ill driva a bit and put it in park if i sit for 5 seconds the starter will engage then put it in gear, turn it off and then i can put it in park with out it engaging. afraid to leave it like this dont want it to try starting in the middle of the night and come out in the morning to a dead battery or possibly fry the new starter if it is constantly engaging when i am driving. i kinda went thru other post but wasnt sure. could it be the neutral saftey switch? or is it on the new starter? im guessing i have a short somewhere possibly but dont know where to start looking.
thanks for any advise or help anyone can give

 

think i found were the problem is.... in the fuse block under the hood. either have a bad relay or a short in the block some where, but replaced it with another relay and it wanted to start without the key even in the ignition. so at least i know the source of the problem but still if any other hlp will be great thanks