I have no way of knowing whether or not the plane ran out of fuel. I'm assuming they kept some fuel, e.g. in case they didn't stick the landing on the first attempt.
The plane did not run out of fuel. If the plane had run out of fuel, the flight crew would have prepared you for a potential crash landing. There would be no question whatsoever. It would have made national news. The plane and crew would have been grounded pending investigation by the airline and the NTSB, and not gone on to resume its journey shortly thereafter. Hell, everything else aside, it would have sat dead on the runway, unable to taxi, while passengers disembarked on the inflatable slides.
Your plane had plenty of fuel. It followed established procedure where they waited for as long as they could, diverted when the fuel situation warranted a change of plans, and landed at the alternate airport with more than enough fuel for at least one go-around and likely two.
This bit isn't right. They would have brought a tug out to the runway and towed the aircraft to a remote stand, then used a staircase.
The slides are only used if there's imminent danger of fire. People often get injured using them.