Run backwards? Never heard that and can think of no mechanical reason for them to do so.
The noise is largely unavoidable. Lacking spark plugs and having far higher compression, their fuel/air charge doesn't ignite shortly before the top of the piston stroke as happens in a gas engine. They squeeze the heck out of the charge and it ignites when it ignites. With the piston still pretty far down the cylinder and forcing its way up against the "explosion".
A lot of engines can be made to run backwards, btw. 2-stroke engines, with their much simpler equivalent of a "valve train" and ignition closer to TDC than a 4-stroke run backwards nearly as well as they run forward. An old favorite practical joke of mine was to bump-start a motorcycle backwards, put it in neutral, and hand it to a friend to take a spin on.
A 4-cycle engine, with its ignition controlled by the camshaft or crankshaft, isn't so easy to get running backwards. 13 degrees BTDC becomes 13 degrees ATDC if you try to run it backwards, and if it'll run at all like that, it'll do it poorly.
It seems to me a diesel wouldn't much care which direction it's running in, though. Aside from valve timing, the fuel ignites when the piston squeezes it enough and wouldn't care which direction the crank is spinning, as long as the piston is on its way up and squeezing the fuel/air charge.
