How many problems does my shed’s 240V receptacle have?

I have a detached shed that was wired by somebody who evidently thought codes were just a friendly suggestion. I'm slowly trying to correct the electrical sins as I find them.

In this shed is the following 240V receptacle:

The receptacle is wired as follows:

The wire that feeds it is 10/2, with this stamped on the side:

E30445 (UL) AWG 10-2 WITH AWG 10 GROUND TYPE UF 600V SUNLIGHT RESISTANT

And that's fed from the following double-pole breaker:

This receptacle is the only thing on the circuit. Total wire length is roughly 80-100 feet one-way.

As I understand it, I have the following problems:

1. It looks like the receptacle is a 10-30R, which as I understand is frowned upon today because it doesn't provide a ground prong.
2. It doesn't seem okay to use the ground wire in a 10/2 cable as the neutral.
3. The breaker seems way oversized for this application, unless I'm misunderstanding how current works with double-pole breakers. It's not clear to me if "internal common trip" changes anything.
4. Other problem(s) I'm not aware of?

I'm looking for the most reasonable way to make this safe and code-compliant, bearing in mind that I don't even have a use for this receptacle right now. I know I always have the option of removing the receptacle from the wall, pulling the breaker out of the panel, and capping the wire at both ends. I'm curious what it would take to fix it right, however.

Bonus question: Does anybody have any idea what purpose a 240V receptacle in a shed could serve? My guess is the previous owner was using some kind of heater or heavy-duty tool — what could it have been?