The proof marks are Birmingham post 1904. BP BV NP should all have a crown over them. They are the post 1904 Birmingham proof marks. BP is for definitve proof, BV is view proof and NP is nitro proof.
The 29 is the bore diameter 8 inches in from the chambers (I think), the diamond with 28 and C means that the barrels are chambered for 28 gauge shells.
The NITRO PROOF 5/8 means that the gun was proofed for a 5/8 oz service charge. I'm not sure if this is the 2 1/2 inch load or not.
The serial number is a bit odd. Are you sure it is 18308 and not 28308? According to Brown's London Gunmakers 18308 does not exist since the serial numbers jumped from 14512 in 1887 to 20088 in 1888. One explanation is that there might be a different set of numbers for odd gauges but this is unlikely.
