The car is trying to start when connecting the battery without the key

The starter relay in your fuse box could be welded. I would try removing it and seeing if it stops. If it doesn’t stop, there is a short to positive in the wire going down to the starter solenoid. If it does stop, I would try installing a different relay; often the horn relay or some other relay will be the same as the starter relay. If when you put in a known good relay, the starter still turns when you aren’t trying to start it, we’ll know it’s a problem with the control circuit to the relay, most likely a key switch.