It the metal is grey and the pots are fairly heavy, they almost certainly are what was called "aluminum" in the US from about the mid 1930s and on. Older than ca. 1945 there is the possibility that they could be any of a variety of loosely defined "pot metal" materials, and there is no specific "list of ingredients" for those.

By the time of the mid 1940s, aluminum/aluminium was a major component in much cookware that would meet the description given, with earlier materials often containing a fairly high percentage of zinc. Very old cookware of this kind sometimes contained a fair amount of lead, but it's unlikely that any this old would still have survived in useable condition.

Note that nearly all similar metals that have been used will melt at about 460F (238C) so don't try to use them in a "Pizza oven."

As to the weight being "like cast iron" I once paid $0.10 at a yard sale for what I thought was a cast iron lid that might fit my skillet - and the bottom, minus a handle, came with it. When I wire-brushed enough of the black off to identify what I had it turned out to be a Wagner Drip-top chicken fryer, solid cast aluminum. An aunt bought one ca. 1946, and my mother had always wanted one; but refused to consider paying the $48 (US - 1946) price then demanded. They're still about the same price, but it's not a week's wage now for most.

The "black" in the stains is carbon, and almost nothing you can use will touch it. If the stain still contains sufficient "grease," chemical cleaners can break up the grease to allow the carbon to be released from the surface.

If the stains/deposits have been there for a very long time, about the only practical way to remove them is with an abrasive attack, and a small wire brush in your Dremel or drill motor would be indicated.

Roughness resulting from abrasive removal, if that's needed, can be quickly smoothed/polished with a "rag" polishing wheel mounted on an arbor in your drill motor, using the appropriate abrasive stick for Al. Polishing wheels and abrasives should be easily found at the nearest hardware shop.

Normal "scouring powders" should not scratch the finish any more than what likely already exists for the "bare metal," should you be successful in actually cleaning down to what's there.

"Clean" alumin(i)um has good heat transfer, but is not a particularly good cooking surface. The residual grease left from using and normal washing will "cure" the surface fairly quickly in most cases, should you be forced to clean down to the metal; but keeping the pots "metal shiny" is not a good goal. If the stains aren't bad enough to reflect unfavorably on your mother's dishwashing practices, my suggestion would be that you give the pots a good sudsy wash, forget about the stains, and tell your friends "that's how my mom had them cured, and that's how I'm gonna use 'em." Work up a song-and-dance routine about the "charm of OLD" and praise the beauty of them.

John