Coach - how long after the second horn was it before the official put the ball down? The rules state the teams should be breaking the huddle on the first horn, and be ready to play by the second. Was there a delay after the second horn while your players were doing "rock/paper/scissors" to see who would throw it in? (Ok, just kidding.) But if the second horn sounds, you're still in the huddle giving last-second instructions, then finally break the huddle and the players walk all the way down the court, get there, and there is still confusion as to who should throw it in - that could use up another 20-30 seconds after the horn. That would be an advantage to your team to use more than the 30 or 60 seconds for the TO, especially if the other team came out at the horn and was waiting. So, to answer the question as to whether the official was too quick: it depends.
As to your other questions:
- A team does not lose the right to run the endline after a TO.
- I do not believe it is required of the official to signal that the player can still run the endline. Many officials do; however I've had some tell me it's the players' and coachs' jobs to know whether they can run the endline, and it's not our job to supply coaching information. (I lean towards signalling, just to remind myself as well as the players.)