You can switch to an Inferno build to get around the ship and weapons limits. It also has a higher textures-per-submodel limit, which IIRC, I've found many of your models ride the limit on that... at least the ones I'm using. Switching to Inferno builds however, make the pilots you access with it, incompatible with standard FSO builds. So, what you CAN do is switch to Inferno builds for your own purposes, but should you be working towards a campaign using these ships or something, you can plan for said campaign to become available AFTER the ship limits have been made dynamic, by which time everyone will have to convert their pilots. Also, the most recent Inferno build was from 2006/11/30.
For this:
Warning: For ship 'GTVBS Archangel MK2', detail level mismatch (POF needs 5)
It appears as though your table file references 5 LODS, but the model has... something other than that. Change the table to match the model.
For this:
Warning: Unable to find a sufficient number of bitmaps for this mission's background. The background will not be displayed.
This may be that you're opening a mission which you made with a different background list. Open up the mission in Wordpad and scroll to the bottom to see what backgrounds you've selected, then make sure the images themselves are there, and that they're referenced in the stars.tbl.
For this:
Warning: Couldn't open texture 'shieldhit01a' referenced by model 'PersAdv.pof'
It seems as though its trying to open a shieldhit01a texture on the model itself. I'd open the model in PCS and see what textures it references.
Not sure what to do about the Ballistic Primaries thing.