I don't feel qualified to comment on most of your questions, but as no-one else has answered yet I'll offer some thoughts which may or may not be relevant. My photographic involvement on construction projects is fairly peripheral, and my contact comes mainly from me asking permission to take photos, and only a little from being hired to take photos or movies.
Progress photos and videos are becoming part of the contract* on large jobs, and there may be conditions about the number per week, file type and size (modest), and presentation (digital and paper) - these appear to be heavily biased towards digital capture and storage. You could be competing against a graduate or assistant engineer staff member, for example, who happens to be interested in photography and who appears to cost the company less than you do. If you need to be escorted on site by a competent staff member then that makes you appear less attractive to the site guys, but other departments probably won't consider it. You need to charge whatever makes it worthwhile for you, of course. You would need to clarify the terms under which you would get any necessary safety or site awareness training (you pay them / they pay you / nobody pays).
Photos for presentations and brochures etc are a very different matter. Photos of prestigious or interesting projects may be widely reproduced, so there is a balance between initial fee and reproduction fee, with the ownership of the rights and your willingness to police the reproduction of your snaps to be considered in there.
QA Photos have done very well in this field, having made a name for themselves by working on the Channel Tunnel. There's a lot that a good photographer can offer to construction projects and it is worth thinking big. For example, time-lapse photography is easier than ever and the results seem to go down well. Hey, a time-lapse movie of a top-down construction job could be the next great piece of conceptual art.
* often in the Engineer's or Architect's contract, not always the Contractor's.