If the gun is marked 2-3/4 on the barrel, that is the maximum length shell that the gun will shoot.
1100 is a Remington, not Browning.
The 1100 designation for a Remington shotgun is the model number. Remington makes the 1100 model in a trap version and a field version.
with the L prefix to the serial number,this would indicate that your model 1100 Remington shotgun was made in 1991.
Visit the Remington web site.
i am pretty sure they are 3" You can shoot 2 and 3/4 in.shells in the 1100 3"mag but, the shot weight has to be at least an ounce and 1/4 for it to cycle {fire,eject and chamber the next shell} properly.
400 dollars
You can request an owner's manual for free at the Remington website.
100-1000 depending on specifics
Best left to a gunsmith
150 mint condition
At least $150 if is in good condition more if it is a 20G
100-400 USD depending on condition.