The 'K' is Remingtons code for the Model 1900 shotgun. I don't think they've figured out what the 'X' stands for yet,,perhaps more recent info has emerged though.
There are several letter & number code stamps (E for ejector,,'D' for Damascus are commonly seen on the 1900) but most have gone un-identified. Some have stated the 'K' stands for 'Field Grade' but I really don't know.
The '///' marking is another. Some feel it indicates choke, but it doesn't seem to follow through in each instance. Seen quite often.
The '30' and '25' are pellet count indicators. Add a '3' in front of each. That would be the # of pellets inside of a 30" circle @ 40yrds with the load indicated on the hang tag provided with each gun when shipped. The tag also had these pellet count #'s & the shot size used written on them as well as the guns barrel length, weight, gauge & serial number.
Both chokes are probably Imp Mod in the gun by their standards but you have remember they used fibre wads and paper case shells. Modern loads with plastic cases and wads and a different shot size/hardness, powder, etc can change choke preformance.
2 5/8" chambers were the norm at that time in 12ga I believe.
Yours was mfg in 1908. Model discontinued in 1910 or '11.
There're some here with a true collectors interest in Remington doubles and may post some better, more up to date info than Ive been able to give.
