Could you drain a battery with only one terminal connection?
Your questions are ultimately about the distinction between circuit and charge models of electricity, and the degree to which certain things are best understood in the concept of one versus the other, though of course the underlying physical laws which those attempt to explain are the same regardless of situation.

1.&quot;A current must always return to its source&quot;
The first statement statement doesn't make sense in regard to lightning

Lightning is typically thought of as being caused by an excess/deficit of charge in a region of the atmosphere relative to the earth.  That's not particularly a &quot;circuit&quot; explanation, but one could also view the cloud-earth system as a giant capacitor suddenly shunted by the conducting plasma channel of the bolt, in which case there actually is a traditional circuit briefly in existence.
It's natural then to ask how the capacitor became charged in the first place. That's a very interesting question more in the realm of atmospheric science, but possible ideas for net charge beyond the air movements creating local concentrations might include slow diffusion of electrons / ions, or the fact that opposite polarity lightning happens too (wikipedia) - more rarely, but with typically an order of magnitude more charge transfer.

or ground faults

These actually are fairly simple circuit phenomenon, as the mains power system is referenced to literal ground stakes driven into the earth, meaning that the intended ground, the transformer secondary, and the &quot;fault&quot; ground form a complete circuit.

2.&quot;Current will flow if there is a difference in electric potential (a voltage difference)&quot;


If I had a battery suspended, and took a conductor from the positive terminal (conventional current) and dug it into the ground, would current flow? I would think so as a potential difference has been created with a clear conductive path.

The key question you need to ask is if there is a potential difference between the positive terminal of the battery and the ground.
What the battery is intended to do is to create a potential difference (and one able to supply meaningful current) between the positive and negative terminals.  There's no path to ground from the negative terminal, so in a circuit sense, no current will flow.
Of course just like a cloud, the battery could (and probably will, at least if you handle it with an insulating tool) initially have a net charge different from that of the earth, so much as in the lightning situation you could get a brief current flow when you initially connect the wire.  But the charge on your battery will be tiny; the battery-earth system has little capacitance so this would be a very small, brief current.  If you drag it across a carpet in winter, you might get a noticeable shock or spark from the discharge; in an unlucky case you could destroy the gate oxide of a delicate semiconductor like a MOSFET.  But there's nothing in such a system which can provide a continuous current flow in the usual concept of circuits, because there is no complete path and no other mechanism to replenish the capacitive charge.  Once the initial capacitance of the system is discharged by the wire, there is no longer any potential difference across it, and no more current will flow.