T after "end" of game...inconsistency in the rules?

[Brad]

My question is, exactly what does "no way to determine" mean?

Basically it means that without shooting the technicals you wouldn't have overtime, but by shooting them you might have overtime (depending if they are made or not) so there is "no way to determine" without administering the free throws.

Suppose we have a 2 shot technical after the end of the second half. It's clear that we shoot the technicals now if the shooting team is down 1 or 2 points.

Right.

Do we shoot now or at the beginning of the overtime if the game is tied?

The beginning of overtime. You can "determine" that there will be an overtime, as the score is tied -- you do not need to shoot the technicals in order to determine if there will be an overtime period.

If the shooting team is down by one point and makes both shots, is the game over?

Yep.