Yes, "Cop Shop" means police building. Here in Oregon they are all posted and the signs have no force of law as state law specifically exempts CHL holders from any and all local ordinances attempting to regulate firearms. Non CHL holders can not enter public buildings with a firearm (loaded or unloaded).
Every state is different, here in Oregon you can not go into the "secure area" of a jail. If you are in the lobby or offices you are legal, if you want to enter a holding cell (or prisoner processing area if a large department) you would have to leave the firearm outside.
K-12 and college campus's can put up all the signage they want here, the signs have no force of law. If you are asked to leave and don't then you can be trespassed. This is currently a point of contention in the state as the schools all have policies prohibiting firearms but they also generally say when asked "CHL holders would be exempt from our policies" but in practice they trespass and/or expell lawful carriers. We currently have a case in the courts where a student, Iraqi vet, was arrested by local PD after security detained him for a firearm....charges were dropped "in the interest of justice" by the DA but the state university expelled him and the university system said he was "not welcome in any university" in the state. Lawmakers were furious - well the non anti's anyway. That case is in the civil system and will likely cost the state a chunk of change as he was expelled for some time until his attorney convinced them to readmit him until the case was settled.
As for "trespassing if caught", the signs are not relevant. Only if you are personally told to leave, and don't, can you be trespassed. The "open to the public" (ORS 164.265) is any and all public buildings (i.e. government), businesses open to the public, and the like. ZThe meaning is that if they are CLOSED and you are there, it's trespassing, if they are open, you must be TOLD.
Our laws are simple, in plain english (even though we have a ton of Commiefornians who have immigrated here), and can be printed on 3 sheets of standard paper and easilly carried by the open or concealed carrier. ORS 166.170 though ORS 166.380 are the applicable sections with 166.170 being pre emption and 166.173 giving ONLY cities and counties the ability to regulate loaded (but not unloaded) carry for those who do not have CHL's.
Like I said, I thought with the passage of AZ's Constitutional Carry that the laws there would be more lax than here but I'm finding that there are far more restrictions than I would think would come with something called "Constitutional" carry.
However, AZ is a far sight better than most other states and has a hardworking group seeking to make it even better. I have no doubt that in the near future Oregon's liberal gun grabbers will make inroads while those in AZ will be heading for other states as your local advocacy groups make more and more progress.
Who knows, by the time I graduate, it may truly be Constitutional Carry in AZ.
