If I was a new player, playnig against 3/3 easier ais, I honestly wouldnt know how to read any of the information beyond 'ohh, attack? lets get a higher attack value', making the ship statistics the only useful set. (again, with potentially build costs in the proper context.)
(additionally, my first game was against a 7/7 pair of random moderates. Ok, well, I played the tutorial completely through)
Civ's tooltips honestly have their own tooltips in them to help you out - When you select a spearman, the info card pops up with more tooltips (like +bonus against mounted units, or whatever rank buffs it has) I really dont think you could apply this theory to aiwar..
And back to aiwar, as an experienced player I *need* basically no tooltips, with the main important bit being ship statistics (damage/speed/hp/hull/etc), multiplayers, and to a lesser extent, immunities. I am sure we could throw in a 'advanced tooltips' hotkey, to give you even more stupid amounts of information (possibly even always showing extended tooltips while paused?)
As for the dreadnaughts doing splash damage, that is something that probably should be mentioned in the attack info (similarly to engine damage, or ire damage), for example below.
Attack: 1,200,000 Splash Damage: 300,000 Splash range: 2,000