1. Surely those concrete pillars are marked on the map as 'Limekilns'? I think the chalk was excavated from the pits, brought to the kilns and baked to make cement.
2. The narrow gauge railway I mentioned is marked as 'Tramway'.
3. As for the tunnel, I take it you mean the dashed line. It's a bit too out-of-focus for me to read the lettering but I doubt if there's a tunnel there.
4. Tell what I'll do. I live only two miles from there on Blue Bell Hill, when I have time over the next few days, I'll pop down with both our maps and actually see for myself.