Zero danger as long as you don’t connect something other than a ground or shield to these.

No. They are indeed used for power only.

But technically you could use them for data or small signal.

Nothing looks burnt here, just heat marks, which would be totally expected after a few decades if the appliance heats a bit during normal use.

Capacitor like these rarely fail for no reason and if it was subject to over voltage you’d probably have a lot of other things fried, they’d be some of the last things I’d check.