Who owns them?
Spurs Sports and Entertainment owns the Spurs. It's led by Peter Holt who is the CEO of HOLT CAT, the largest Caterpillar dealer in the US. Caterpillar is known for those big tractors.
Does ownership own other teams and facilities
Holt also owns the WNBA's San Antonio Silver Stars; the AHL's San Antonio Rampage which is the affiliate to the NHL's Phoenix Coyotes; and the D League's Austin Toros. He doesn't own the AT&T Center which houses all of the team except the Toros.
How is ownership doing?
The Spurs have packed the house over the past decade, and for good reason. They have been one of the NBA's best teams over the past 10 years and they're doing it again this year. The other teams Holt owns however may be the downside to an otherwise well run organization in a "non-big time market". Ticket prices are a bit more expensive than I'd like, but the Spurs are winning a lot every year.