Keith has explained that these RED spots within the metal are not an iron oxide.
Well, that's not exactly what I said. I'll try to elaborate without any name calling or eyeball gouging...
When we polish a set of twist or Damascus barrels for initial finishing or for refinishing, we say they are "in the white". Everything is very bright and uniform in appearance, because we have polished off all surface crud and oxidation. Since the iron and steel look so similar in that condition, it can be difficult to even tell they are pattern welded barrels.
Then we apply our secret rusting solution of choice, which causes our shiny white barrels to rust very quickly. A highly polished surface will rust more slowly, because there is less surface area for oxygen to react with. Under the right conditions, with a fairly aggressive rusting solution, they can be completely covered in a uniform reddish brown ferric oxide in only a few hours. This is then carded off. Or in the case of black and white, the barrels are boiled in water to convert the reddish brown ferric oxide to a black ferro ferric oxide, and then that layer is carded off. Subsequent applications and carding, or "turns", gradually begin to color the surface either brown or black.
At this point, it can still be hard to tell if our barrels are pattern welded, because everything is pretty uniform in color. But the oxides that impart the brown or black color do not bind equally to the steel and the iron. And they are even less tightly bound to the so-called "grays". So at whatever point we etch our barrels with our ferric chloride solution, the parts that have this oxide less tightly bound become much lighter in appearance, and that is what gives us the contrast between the iron and steel that we desire. It also makes the "grays" stand out and become more visible too. The controlled oxide we apply as a barrel finish gives us a very fine grained coating that can actually inhibit normal rusting, which is one of the reasons we brown or blue(black) our guns. And the gun oils or wax we apply further inhibits atmospheric oxygen and humidity from rusting our barrels.
But when our barrels are somewhat neglected, such as the gun in this thread, common red ferric oxide, or rust, can form. However, it will form faster on those areas that have less of the protective oxide that we applied in our blacking or browning process. Since the "grays" are more resistant to our browning or blacking, and had protective oxides removed during etching, over time they become more susceptible to a surface coat of common red rust, when our protective coat of oil or wax is gone.
Since this rusting due to neglect is only on the surface, that's why I said earlier that it typically comes off pretty easy with a few minutes of polishing with 0000 steel wool and WD-40. From what I see in the pictures, I don't see that rusting as dangerous. It is what I don't know about the silver spots and the bores that makes me unable to even guess about whether they are safe to shoot. It would be nice if the OP came back and filled in some blanks.
So our pattern welded barrels are a complex mix of steel and iron that is laced with varying amounts of inclusions. Over time, the oxides that form the finish which was applied may also change. And the rate and amount of this change depends upon what we do to protect them from oxygen found in air and moisture. This is when we find that not all gun oils protect equally. When there is a lot of change due to new oxides forming, and old oxides converting to ferric oxide, we politely call that rusting a "patina". The change will differ in a humid Louisiana environment and a dry Arizona desert climate. Although the "grays" may appear to have turned red, a quick swipe with a file or sandpaper would prove that this red coloration is not internal. The red color is due to ferric oxide forming on the surface of the "grays" because the "greys" contain a high percentage of iron. But the "grays" mainly have not been converted to ferric oxide. If and when they do develop such deep rusting, the barrels will become useless.
