: 1. Did they have lume on the dials? Mine doesn’t have any and it
: seems odd to me that there is nothing. From the photos online
: that I have seen its hard to tell if they do or not.

Yes, they had lume "sticks" like the PVD Monaco, that ran the entire length of the white hour marker on the dial. They are notoriously prone to breaking and pretty much every dial you see has lost them to one extent or another.

Look at the example above and you see them intact at 3, 4, 5 and 7, partial at 10, 11, 12, 1 and 2 and missing entirely at 8 and 9. Yours is following the pattern of 8 and 9! Arguably, totally missing actually looks better than partial sticks and it's very rare to see one intact:

: 2. Did they have serials and ref numbers in the same place as the
: other barrel Carreras? I have a ref number on the caseback that
: says R110 571, and nothing on the ends of the case above the
: lugs. I thought the ref number was 110.571 NC

The full reference is indeed 110.571 NC but the suffices weren't put on the cases, so they could be used for a variety of dials. In this instance, only one dial is available anyway, of course. Both reference numbers are absent on the examples I've seen, or at least not visible - they are faint on barrels anyway and they are either occluded by the PVD process or not there in the first place. The gold plated examples have visible references but that was a much better understood process than PVD in the mid-70s. The original PVD finish was a bit rougher than on yours but then they had a rougher case surface underneath too, rather than highly polished - looks like you got really good adhesion with the PVD despite that. At a glance, it now says 110.571 to me, whereas the polished one just made me sigh...

: 3. And lastly were there pvd buckles for straps or were those just
: stainless like normal?

Yes, some had PVD sun buckles but in a few years they typically looked like stainless steel with a few black patches on! A steel buckle on black strap works too, as it echoes the pushers and crown that were left steel to contrast with the PVD case.