Check the image directly using DISM. Also, make sure the image was successfully distributed to the DPs and that the image on the DP is the same image.
There's no way to add Office updates directly to an image however you can add the .msp files to the Update folder of the source files and these will be added automatically by Office setup -- this assumes you didn't put Office in your image itself though. If you've done that, simply rebuild your image -- you are using a build and capture task sequence aren't you? If not, why not? This would seamlessly address both of your issues without any real work on your part.
Didn't say recapture, said build and capture. Using this methodology, you automate building your images from a clean OS install (using a task sequence in exactly the same way that you deploy the image). In this way, if you need to update the image, you simply change your TS (if necessary), re-run it and walk-away.
As for activation re-arming, if you are using Enterprise media, there is no limit. If you are using Pro media, then there is a limit of 3 activations/syspreps. In the case of a build and capture, this is meaningless though because as mentioned, it's a clean install every time.