I've heard these from other sources... (B) (C) and (D) below are not in the law.
This section does not apply to a person...if...all of the following apply:
(a) The person is carrying a valid concealed handgun license or the person is an active duty member of the armed forces of the United States...
(b) The person leaves the handgun in a motor vehicle.
(c) The handgun does not leave the motor vehicle.
(d) If the person exits the motor vehicle, the person locks the motor vehicle.
Read the law again, many of the nuances above are not true, and many left out.
 it doesn't say handgun in the law, it says firearm or ammunition. Shotgun and rifle are included in the law as permissible, if they're in a locked container when you're not in the vehicle.
Not for transporting into a school zone under 2923.122, which is what sd790
was referring to. The exemptions under (D)(3) and (D)(4) specifically apply only to handguns.
(3) This section does not apply to a person who conveys or attempts to convey a handgun into, or possesses a handgun in, a school safety zone if, at the time of that conveyance, attempted conveyance, or possession of the handgun, all of the following apply:
(4) This section does not apply to a person who conveys or attempts to convey a handgun into, or possesses a handgun in, a school safety zone if at the time of that conveyance, attempted conveyance, or possession of the handgun all of the following apply:
 the firearm and ammunition has to remain in the vehicle while you are in the vehicle, but it can leave the vehicle so you can lock it in a compartment ON the vehicle (an important wrinkle for those of us who ride motorcycles),
No that's wrong. There's no provision in the law allowing you to exit your vehicle with the firearm while in a school zone.
The exemption in 2923.122(D)(3) only applies if (among other things) you are not "onto school premises" (aka in this case, the parking lot).
The exemption in 2923.122(D)(4) only applies if (among other things) "The handgun does not leave the motor vehicle."
 you can't leave ammo on your person, so spare magazines/moon clips/speed loaders/etc locked in/on vehicle,
Please identify what law you think prohibits you from having ammunition on your person in a school zone.
 it has to be in a LOCKED container in or on the vehicle, and left in unlocked glove compartment doesn't meet the requirement,
Again, the section of the law on having a firearm in a school zone doesn't say that. It sounds like you're confusing the parking lot protection portion of the law with the school zone changes.
 the law doesn't say your vehicle has to be locked,
It explicitly says that, as noted above. Again I think you didn't realize that sd790
said he was talking about the school zone changes in the new law.
 the private vehicle has to be owned by the person, so no rental car or carpooling,
Please identify where it says that, as far as school zones. I don't think it does.