Yes you are correct. They have not published the actual airplane weights. And you are correct in saying they probably not near tire speed limits upon rotation. However, techniques around here would amaze a person. I was using that as a example of what could cause a nose wheel tire to explode. Many many other factors have been known to chase a nosewheel tire to expand and explode in the wheel well.
Sure, like debris on the runway.
Anyway electrical fire is further down on my list because it doesn't fit the rest of the scenario -- the lack of distress calls and the fact they flew around for several more hours, apparently not incapacitated (at least initially). The graphic of their known flight path shows a zig-zag pattern consistent with finding an airway to join, not with a descent into a recovery field. And reports had them flying directly over known navigational waypoints after their initial turn away from course to Vietnam, something they would have done with use of the FMS and the autopilot. If they'd been proceeding direct to a suitable field after the first turn then why all the subsequent turns over such a long distance with no radio calls? These various other facts don't mesh with the fire scenario.