Parking lights won't shut off

I recently had a issue with a fuse blowing for my parking lights and dash lights. Last night I changed the fuse for the second time in 3 days and all of a sudden the truck would not shut off. I turned the key back on and turned the head light switch on and it turned the engine off. Then I started the truck and turned the lights on, but the headlights would not come on. I had to drive home with the fog lights on. When I got home, the truck turned off fine, but the parking lights and tail lights would not go off. I had to disconnect the battery. I did notice the dash lights and tail lights started blowing the fuse after using a friend's trailer. And also, my check engine light came on a day after. But after reconnecting the battery and driving, my check engine light still hasn't came back on so I can't run a code reader.
Hopefully someone on here can help. It is a 99 ranger 3.0 4x4 xlt off road

Welcome to TRS

I can't see all of it being related.

The head lights, parking lights and brake lights have power all the time, key on or off doesn't matter.
So there is no cross over electrically that would keep the engine running.

Blowing fuses when hooking up or pulling a trailer is not uncommon, trailer wiring is a world unto itself.
You will need to inspect the trailer wiring at the back of your truck to make sure there are no shorts, which there probably are if you have had to replace fuses AFTER unhooking the trailer.
So get out the Volt/ohm meter and test for shorts to Ground

In 1999 fuses #3 and #7 in cab fuse box are used for trailer lights only, if...........its a factory trailer light system, not a DYI add-on
Factory trailer Parking lights use fuse #35 and separate relay

Fuse #11 in engine fuse box powers trucks parking lights

So which fuses are blowing?

And do you have power windows and door locks?
Wiring is slightly different if you do

Engine not shutting off will be an ignition switch problem.
How does the key switch feel, is it loose or sticky, or............??

Under the steering column above brake/gas pedals is the ignition switch
It is a Slider switch, when you turn the key a long rod slides the ignition switch into its 4 positions, ACC, OFF, RUN, START.
OFF position cuts power to the PCM Relay, when PCM relay is off(open) computer loses power, fuel injectors lose power, fuel pump loses power, spark loses power.
So only way engine could stay running with key turned to OFF is if the ignition switch didn't cut power.
As said the lights do not run thru the ignition switch, well turn signals do, but not parking, or brake, or head lights, so I don't see a cross over.

The park light relay should be in the "relay box" up under the dash by the ignition switch, not sure on a 1999 Ranger, this relay could be stuck closed so parking lights would stay on all the time