Re: Iver Johnson info request
Welcome to TFF, and thanks for the detailed description.
Your 2nd model .38 was made in 1906, the only year serial prefix Q was used.
It's a black powder model and caliber is .38 S&W. (A .38 Special round should not fall all the way through cylinder, but should fit loosely, as .38 S&W is slightly larger diameter)
It should probably be retired, as use of current smokeless powder ammo will rapidly loosen the lockup.