...The Dominion War battles looked like uncoordinated melees based on "every ship for herself" to the outside. Is that a typical way for Starfleet to fight?
I blame Sacrifice of the Angels for that popular perception of DS9 battles. Early in the battle, the Dominion blocked Starfleet communications, meaning no fleet coordination and massive disorganization that made many Starfleet vessels easy targets. But it's also testament to the strength of those vessels, considering that O'Brien only managed to take down that jamming field after several hours of combat, and Starfleet still had ships that got through the blockade (with some last minute assistance by the Klingons, of course). So to answer your rhetorical question: No, i don't think that's a typical Starfleet fight!
In the subsequent big fleet battles, Starfleet seemed to have much better coordination, ie squadron formations at Chintoka and Cardassia (though I recognize that they're far from perfect -- dramatic licence being what it is). A couple of my favorite shots include the Defiant, the Hood, a Miranda and a BOP on an assault run in "Tears of the Prophets," and a Galaxy-class remaining stationary but providing fire support, complete with the Defiant and various Federation fighters zooming around, in "What You Leave Behind."