Sorry, I answered this a few days ago on the forum and apparently, my post got eaten and is in the ether. I'll try again.
1). Effective range sets the basic "knee" in the hit calculation curve. The actual "final" range is a function of a bunch of factors hard and soft. This is for tank guns of course. Other weapons have other systems for resolution. Pen values are also scaled up or down from effective based on a curve calculation as well. A fairly flattish curve since most modern sabots don't lose much pen over long ranges.
2). Stabilization offsets or reduces hit chance penalties if the attacked and/or defender are moving. The better the stability the more penalty gets reduced. Fire control and gun accuracy act to adjust the "final" range of the shot improving or degrading hit chance depending on the quality of the equipment and the effective range of the system.
3). ERA is just a set special. You have ERA and then what type. Higher number is a better type. 1/2 is the early HEAT only EAR and 3/4 is the better Kontact 5 ERA that can effect kinetic rounds as well. The +/- indicates coverage. I believe "+" includes top and "-" is frontal only. Composite armor is a factor against the base armor value versus HEAT rounds. Each Point is an additional 25% protection over the kinetic value.
4). Not really sure here is that special is even processed for an AP shot. If it is, it would reduce the effectiveness of the ERA reduction.