1) yes, any license issued pursuant to PC 12050 is an exemption to all of PC 12031 (the statute for the loaded condition of a firearm)
2) Yes, sort of - if you discharge a firearm in a no discharge are you could be prosecuted under that statute. However, I know of no statute which prohibits the carry of a firearm in CA excepting 171b, 626.9, and 12025
Please keep in mind that there are two relevant areas of legislation in CA. A) The carrying of firearms; B) Whether or not firearms are loaded.
3) What you are referring to is a very rare (read nonexistant) option for a Chief LEO to issue an exposed carry permit which is good in 1 county only. However, keep in mind that the carrying of a concealable handgun openly in CA is not (generally) prohibited. These permits can only be issued in counties with a population less then 200,000.
4) There is not 'stop and identify statute' in the state of CA. However, if you are actually arrested you must identify yourself
5a) If the Serial Number is readily evident, they may check its records, but they may not detain you in order todo so unless they have reasonable articulable suspicion that you have (or about to) commit a crime.
5b) A license issued pursuant to PC 12050 is an exemption to PC 12031
Yes, CA has Gun Free School Zones - See PC 626.9. PC 12050 is an exemption to the GFSZ.
An Airport -legal in the unsecured area
Bar - legal
Church - legal
Entertainment Event - legal
Poltical Event - legal unlessthe even is a 'labor strike' type of event
Park - generally legal
Public Building - not legal without a 12050 license - see PC 171b
College/University - I'm not positive on this one but I think its generally legal. Edit: not legal without a 12050 license - see 626.9
CA has preemption at all levels for those areas which 'encompass the totality of legislation' Generally speaking this covers the carrying of arms.
edit: p.s. I typed that all up in a real hurry, I should be corrected shortly if I missed a direct question.