here's a fairly descriptive dissertation on roman army dispositions and tactics.
linky
per this the normal seperation between ranks and files was about 6 feet, which was failrly spacious - you need room ro swing a pilum when you are about to throw it & need room to swing your sword & sheild about without interfering with the guy next to you. other sources say the horizontal spacing of rankers was closer to 3 feet, with the 6 feet spacing of the filers behind you to allow for missle throwing.
the left side was your 'weak' side as it was weighted down by the shield, so fighting was biased to the right, and your general would try to get some sort of attack on the enemied left flank to disrupt their formation. romans fought as a team rather than as individual duellists, so you'd help the guy to your right by zapping his opponent whose right side was more exposed (similar to what brit bayonet men did to the scots at culloden).
romans won because they were more disciplined and fought dirty. barbarians lost because they fought with their personal honor in mind and wanted the glory of besting their opponent one-to-one in a duel. the romans also won because they understood logistics.
a roman battle would normally be done at the advance rather than staticly awaiting the enemy, they would addvance completely silent -when close they'd throw their heavy pilum spears in two volleys which would shock the advancing enemy to a halt, the romans would draw swords, and then shout and charge the enemy. usually the enemy wouold break at this point as the buzzsaw of the roman gladius hit them. slingers, archers were not heavily employed in the traditional late republican/early imperial armies.
people actually killed in the battle lines were in low numbers, the majority of casualties happend when one side broke & started to run, with the victors mowing them down as they tried to get away..... and as in most armies up until the advent of penecillin, more people died of disease and infection than in battle. roman medicine and wound treatment was far in advance of the barbarians, so they lost fewer men that way too.
the romans really epitomized the slogan 'who dares wins'