First off, the Colt 1860 Army was a large, six shot, 44 caliber revolver.
Like this Pietta replica of the 1860 Army.
Yes, the 1860 Army did come in a version with fluted cylinders, but the flutes extended the entire length of the cylinder, unlike the OP's revolver.
The 1862 Police revolver was a FIVE shot, 36 caliber revolver. Smaller than the 1860 Colt, hence only five shots. But the 1862 Police revolver did have a similar, aesthetically pleasing loading lever assembly as the 1860 Army, so confusion is understandable. The 1862 Police came with 3.5", 4.5", 5.5" or 6.5" round barrels.
That is the correct location for a Colt serial number, it is not an assembly number. Assembly numbers were stamped on various parts after soft fitting and prior to finishing, so the parts could be reassembled with the proper mating parts.
Here is a photo from Uberti's webpage showing the difference in size between their replicas of the 1860 Army at top and the 1862 Police at the bottom.