I believe that Ballistol contains salts of oleaic acid, the oil in linseed oil.

What happens to blued barrels after being oiled with Ballistol and shot many times?

The bore will take care of itself.

What about the blued surface?
Does the Ballistol build up and oxidize?

I have used it for years on all my doubles. Wood and metal...with no buildup at all. Simply wonderfull stuff

I, also, have used it for many years on my flintlocks and modern arms with excellent results. If it's firearms related, and a German made it, it will be excellent!

In my experience, Ballistol can "darken" bluing just a bit. I found this characteristic to be useful when a gunsmith "glare bright blued" a Remington 870 receiver. Repeated applications of Ballistol cut down the glare quite a bit. This characteristic has been less desirable when the maintenance of "bright blue" finishes like those of vintage S&W revovers is an issue. I use other oils on such guns.

I agree that Ballistol is wonderful stuff and I use a lot of it. Its ability to darken blue finishes is about the only characteristic that Ballistol has that I tend to be careful about.