If I understand correctly, a DC circuit powered by a simple battery would not be affected in any way by an earth ground. By earth ground, I mean a copper wire attached to the ground through a long rod in my basement floor.
Thus as far as the three circuits here show...
Have I got this right in my mind?
Yes but you need to be careful.
The symbol you are using doesn't mean necessarily a ground in the sense of earth. Ground is commonly used a synonym of reference. Many simulation tools needs a reference for calculation. It is also the reference from where all the voltage listed on your board will be reference to.
Now, for the other part of the question, no any crazy voltage would make a circuit in simulation. In real life, it's an other thing. You would have to consider your leakage.
the top 2 are exactly equivalent.
No, one is floating, which won't affect the battery or resistor, but can affect some circuits. It will also matter if you connect test equipment to the circuits.
the bottom one will not allow current to flow from the battery, and no amount of voltage, even a ridiculous quantity, could ever make this bottom circuit work.
In the ideal world, yes. No current will ever flow. In the real world, everything is surrounded by air so it will arc if you increase the voltage.
The top two form a current loop from the battery through the resistor, then back to the battery. No current flows into or out of ground. But, only the grounded one (left) will measure voltages to ground. The ungrounded one (right) will not: it's 'floating'.
The bottom circuit has no current loop, so no current flows. But because the resistor is grounded on one side, the battery (-) terminal will measure -1.5V to ground.
