Hey Trailboss

"How close to the localizer and TDZ do you have to be for it to autotune?"

Im not sure exactly how far from the runway you have to  be for the auto tune to work however, I seem to remember that on one of the approaches I made recently, the radio autotuned at 12nm which happened to be a waypoint if i remember correctly.  I'm not sure however if there is a set distance that the autotune occurs or if it is a particular waypoint.

"Does the autotune sense the localizer while converging on it, and then if LOC is selected will it turn the aircraft onto the localizer course?"

As I noted above I'm not entirely sure if the autotune occurs at a set point or distance - I will need to look out for this  but I think it is 12nm - however, I would have thought that the ILS frequency would already have been tuned into the radio prior to intercepting the localizer.
You are correct in stating that hitting LOC will turn the aircraft on the localizer course.

"Does the autotune dial in the closer of the 2 (or more in the case of ATL) localizers?  If you cross the first localizer will it then retune to the frequency and heading of the second?"

Where there are two ILS Runways next to each other, in order for the autotune to intercept the correct glidescope, you will need to program into the FMC which runway you are going to be landing on (ie 5L or 5L) .  This is selected in the Dept/Arr menu.  Therefore, if you were to cross one localiser, the radio would not tune in that runway ILS frequency - it would always have the frequency of the runway you were planned to land on.  Also note that if you were crossing the ILS of a parallel runway this may raise a few eyebrows in the Control Tower.

Try and select a better approach - if there is one available - to line you up with the runway earlier on.

Hope this is useful

Neil