Because the preceding arriving aicraft was a jet, the runway must be clear, regardless of runway length, at the time you crossed the landing threshold. Had it been another single engine, 3000 feet would have been adequet; had it been a non-jet twin, 4500 feet would have been okay; had it been a jet departure 6000 feet and airborne would have worked. All these rules are available for free on the FAA's website....look up FAA Order 7110.65, and look in chapter 3.
As for the crossing traffic, you're mixing apples and oranges. The rules are totally different. Its completely legal for a controller to cross the runway you're landing on at any point that it behind you. In addition, the controller (if so approved at that specific airport) can use LAHSO with aircraft landing or departing an intersecting runway, and here in ATL, we use it to cross aircraft taxiing at the extreme deprture end of the runway while you're landing, by asking you to hold short of that taxiway. All completely legal under specific circumstances.