Based on what you've said here and I'm reading online from avid Marlin collectors, if your gun says "Model 93" and not "Model 1893," it was manufactured somewhere between 1920-1936.
Here's what I found:
Marlin came out with the gun in 1893, as the model number suggests (patented 1887), and until 1919 it was marketed as the "Model 1893." Between 1919-1936, it was produced as the "Model 93." After that, the Model 36 took over.
The "A" at the beginning of your gun's serial number shows that it was from an earlier production, but not the earliest---the guns produced starting in 1919 did not have any letters before the serial number. It seems all these guns had 4-digit numbers, and when number 9999 of a series was made, as it were, they just affixed the next letter of the alphabet to it. I know Marlin made it at least as far as D. So I'd bet the gun's from the 1920s.
(Most of what I said comes from post #5 on this thread:
http://forum.pafoa.org/showthread.php?t=213342)
Whether it's in operable condition or not depends on the condition of a number of parts. I'd take it to a gunsmith or gun shop and have it looked at and ask them. If it really is in "excellent" condition, the answer is probably yes. The barrel says "smokeless steel" because it was designed to withstand smokeless powder pressures.
As for the monetary value of the gun, this article points out that the devil is in the details---there's just so many variations of this model out there:
http://www.gunvaluesboard.com/marlin...rimer-982.html