From Page 4 (left hand side) of the Missouri State Highway Patrol website (printable pamphlet) on firearms (mostly about concealed carry)
In addition to the concealed carry endorsement discussed above,
Missouri now permits any person who is at least 21 years old to transport
a concealable firearm in the passenger compartment of a motor
vehicle. No concealed carry endorsement is required. Under the old
law, the peaceable journey exception to the unlawful-use-of-a-weapon
law permitted travelers on a continuous peaceable journey to carry a
concealed weapon. The peaceable journey exception is still in the law,
and may apply in circumstances where the new law does not (i.e. if the
person is less than 21 years old). Also, any coroner, deputy coroner,
medical examiner, or assistant medical examiner may carry a concealable
firearm upon or about their person without an endorsement.
Note: This law does not affect the law prohibiting possession of a concealable
firearm by a dangerous felon.
And from Page 3:
Q: Does a person carrying a weapon in a vehicle also have to have a permit for the gun?
A: No. A weapon may be carried anywhere in a vehicle, even concealed on the person, under the vehicle exception.
[line]In short, as long as you are 21 years of age or older and can legally own a firearm, you can carry a handgun any way you wish, loaded or unloaded, anywhere in the passenger compartment of a motor vehicle in the state of Missouri. It does not have to be your firearm, you can borrow it from a friend or relative. The pamphlet linked about gives an overview of a lot of the applicable information.
The "Castle Doctrine" Bill can be found HERE. The entire Missouri revised statutes can be found HERE. The Castle Doctrine bill changed several statutes. If you read the bill and refer to the Missouri statutes website to read the entire statute covered you will have a pretty good overview of the Missouri handgun law and lethal force laws.
ETA (edited to add): Welcome to OCDO - hope you enjoy the forum!