Are you talking about a Gun or a Rifle? Please post the question again, except this time please add the model number, you will find it on the barrel. As far as I know Daisy doesn't make a 2006 10 pump BB Gun. They do make several single pump air rifles. However Crosman does make a multi pump Air gun, the Crosman American Classic. It this what you are asking?
I can not find any information about a daisy model R6. In fact as far as I know Daisy dose not use this type of numbering system for any of their air guns or rifles. However Beeman makes a model R6 .22 Cal Air Rifle. Could this really be a Beeman and not a Daisy? If it is, then state the condition of the rifle as Poor, Fair, Good, Very Good or Excellent so I can give you an estimate of value.
As far as I can find, Benjamin made a pump handgun model 112 from 1938 to 1941. I could not find anything on a rifle with that model number.
Type of action has nothing to do with how far a weapon will shoot. Caliber and load is what matters.
It all depends on the rifle, pellet and power source.
Depends on the rifle. Accurately? About 50 yards max.
It all depends on the country, State or location where you live.
the rifle itself will only travel as far as you carry it
If you are looking for the high end of air Rifles then look into the PCP class of air rifles (PreCharged Pneumatic) these air rifles are used in the Olympic games and in serious hunting. PCP rifles are expensive but you get the very best in air rifles. They not only come in .177 caliber but also come in .20, .22, .25 9MM, 45 Cal and 50 caliber pellets. They require a special air pump, Or Hand pump or Scuba tank to charge them to 3000 PSI. This is far beyond the common air rifle. They will cost you allot, in the range of $300 to $3,000. Benjamen currently has a starter PCP rifle called the Discovery. If you are looking for raw power then the Shinsung Dragon slayer fires a 50 caliber slug that is capable of bringing down a deer or moose, it cost $550. If you want a top end Match rifle then the Feinwerkbau 700 Aluminum Blue will cost you $3.395. Benjamin currently has an excellent PCP rifle called the Marauder ($500) that comes in .177, .22 and .25 caliber. The choice is yours.
I believe you question is a little vague. First of all are you asking about .177 caliber or are you asking about any size pellet. They come in several sizes. As for pump, I am going to assume you mean forearm pump. Not PreCharged Pneumatic (PCP) air guns. (More about that later.) As far as .177 caliber pump. Currently Benjamin makes a pump (Model 397) that is rated at 800 FPS. This is about as fast as they get. But don't confuse speed with power. Benjamin also makes a model 392 that is a pump but fires a larger .22 caliber pellet at 685 FPS. it may be slower but it will be harder hitting and will have more knock down POWER. PCP air rifles also store air or C02 but they do not have a forearm pump. They are charged with a special hand pump or scuba tank to 2500 to 3000 psi. These are extremely powerful air rifles that fire pellets up to 50 caliber and will bring down a moose. If you want to understand more about the different types of air guns then see the link below (My profile) and read the section on 'Air gunning."
Depends on exactly what the rifle is, and how far it's disassembled.
As far as I know Crosman has made a 1077 rifle and a 1377 pistol, but never a 1177 model that I know of. However Crosman offers a service to locate repair shops that repair older air rifles. See the link below.