Air guns are not held to any firearms restriction other than age to purchase in Texas that I can find or know of. Act irresponsibly and you will pay the price though. I know people who shoot in their garages and homes! Get a silent pellet trap and no one will know you are shooting. Ebay has a good one for about $70.
No they are not illegal.
No
No
You may have to send it out, there are several shops that make a living repairing and tuning air guns. Do a search for air gun repair on the web or see the link below.
Yes
In some places, yes.
Houston is too far from the equator
The distance from Houston, Texas, to Baghdad, Iraq, is 7,362 air miles. That equals 11,847 kilometers or 6,397 nautical miles.
The distance from Houston, Texas, to Freeport, Bahamas, is 1,041 air miles. That equals 1,675 kilometers or 904 nautical miles.
assuming Houston Texas, 5015.29 miles
London-Houston by air is about 4,800 miles.
The air mileage from Houston, Texas, to Fort Lauderdale, Florida, is 963. That equals 1,550 kilometers or 837 nautical miles.