It all depends on the country where you live
When you say Air Rifle you are referring to a pellet rifle not a firearm. At present there are no 300 Cal air rifle being made.
It depends on the power of the air rifle, Local laws and the location where you live.
Depends on the air rifle. England restricts certain higher powered air guns that have enough energy to be useable as a weapon.
There is no legal limit for PSI for and Air Rifle. Many PCP Air Rifles Have extremely high PSI's and are charged with a scuba tank for mutable shots without a recharge. About Modified: Without taking the rifle apart and knowing what to look for it is unlikely that you will notice any change unless it is obvious from the outside.
There is no legal limit for the rifle in the USA. But you did not state where you live. So I suggest you contact Air Venturi for further information. See the link below for the owners manual and telephone number for Air Venturi in the USA.
You will have to contact the California Department of Justice for a current, legal and correct answer.
Yes, an air rifle is not considered a firearm by Texas or federal laws.
Yes- air weapons are amongst the few firearms it remains legal for a private individual to own in the UK.
Search the web. There are shops all over the place that modify air guns. (air gun repair). They modify the trigger and several of the internal PCP parts for more accuracy. A simple solution is to place a flat soft sponge and FEW drops of Crosman Pellgun oil in the bottom of your pellet tin. This will lubricate the pellet and the barrel, doing so will increase your velocity. Do Not over lubricate the pellets.
First of all, find out what the legal power is where you live. You don't want to break any laws. Then I suggest you contact ARMEX and find out if it is possible, or search the web for "air gun tuners." these are people who modify airguns for a living. See the link below for ARMEX
Depends entirely on where your back yard IS- and the local laws.
Because of the nature of the PCP power plant I suggest you search the net and look for air gun repair or air gun tune-up. There are shops that tune up air rifles and modify them.