Car starts on its own without the key in the ignition

Couple things. Can you get a recording of the engine doing this? Second the most likely thing is a short to power on the wire coming from the ignition switch or going to the starter. This means that the relay is getting power and sending it to the starter or the starter is getting power from a short past the relay. Lastly this could be a shorted relay as well.

So the way to figure this out, is to check power at terminal 3 of the starter relay and at terminal 5 of the relay. If you have no power at terminal 3 then you have a short between the relay and starter on that wire.

Let's start with this and go from there. Thanks

That is great. What was the fix for that issue?

As for the other issue we need to start a new post for that one. I think you did already as this issue and vehicle sounds familiar but we need to keep each post to one topic so that others can find the solution if they have the same issue. Thanks

https://www.2carpros.com/questions/new