Well abilities are easy to tell. You'll see the buffs and penalties on your unit's unit cards (+25% Weapon Range, -3 armor etc.) Before long you'll learn the abilities and thus will be able to tell what ships are responsible for which effects (though if one in particular is causing you trouble feel free to ask).

The Empire tree is the best way to tell which of your ships are being attacked. Even if you have it stacked (which I prefer) you'll see the health bar of the most damaged ship in that type. There is no real way to tell what ships are attacking it without looking, but really you should only take the time to care if its a capital ship.

You might find it useful to get a graphics mod like bailknight's, since it not only makes your game look much better but its makes the particle effects much more noticeable (as well as diversifying the weapon effects, so most weapon effects don't over lap as much).

Just to clarify, this is just part of the unit AI preferring to attack units it is good against, though this is by no means absolute. It also takes into account things like how far away targets are, and while the AI won't focus fire like human player do, they seem to have some additional perimeters for targeting in fleet battles beyond the regular unit AI.