Is it acceptable to trill the G#2 (to A2) with just the annular LH finger? I cannot hear any difference compared with correct two finger trill. Not in my Yamaha YFL674. In the Gemeinhardt it was more noticeable but still small.

probably no difference if your flute is higher pitched and bright, which is what you have, trying playing the two and see if anyone can tell the difference

Not in my case, at least for the moment.

I find it easier and faster to move just the annular while the little finger remains pressed; otherwise both move slightly uncoordinated and the note change is irregular and not neat.

I checked that with my teacher and I felt she did not like the idea, but conceded that the difference was minor, if any. My question is more concerning other problems that this bad habit might cause, perhaps in higher octaves or something I cannot think of right now.

Bad habit? hmmm...
It actually helps to develop independence of finger motion.
I've found no difference in sound between the two ways here.

I only trill the ring finger (well, whatever you would call LH3...LOL). If I trill both then the keys hit at opposite times for some reason.

-Dennis

Fingers' names are a little confusing for me.

I normally name them: Thumb, Index, Middle, Annular (or ring finger) and little finger.

Do the numbers that are being used on some posts, refer to the fingers after the thumb? (i.e LH3 would be the ring finger)?

That is correct.

-Dennis