at the bottom rear underside of the motor, right beside the oil pan.
It is attached to the starter.
YES.
The starter solenoid is attached to the starter.
There is no 2001 S10 with a V4 engine.
Follow the positive battery cable from the battery, it will lead you right to the starter.
On the passenger side of the engine in the back.
Should be on top of the starter - follow the + battery cable
Backside, lower, passenger side of engine.
It is on the left bottom side of the engine towards the back.
Inside the fuel tank
In the fuel tank
It is attached to the starter, just follow the positive battery cable from the battery, it will lead you to the starter solenoid.