I got my first vintage Singer a little more than 2 months ago, I am far from experienced with these. So keep that in mind when I try to help.
In you situation I would remove the hand wheel and the motor cover (like in your pictures) and run it slowly and watch for anything that doesn't seem right. Smoke, noise, anything you wouldn't expect.
But like I said, I am new to this. That is just what I would do. As far as electrical problems like shock and fire you need to use your best judgment on that.
Here's a pic of what I'm talking about.
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