The focus ring in my A1 is over-sinsitive to me, even if I set it to
"Slow". It's enough to virtually touch it, and the reading changes form say
0.2m to infinity. Is it just me, or is it standard?

It is very sensitive. You have to be careful and exacting about the focus. But you can get used to it pretty quickly.

This behavior is normal at wide angle where focus setting is very insensitive., especially in small video sensors domain. Distance readout simply reflects that phenomenon.

As you increase focal length, focus changes become more significant and distance readout together with focus ring follow with increased resolution.

*edit* I should learn to read posts more thoroughly :-\