For ordinary clothing the Roman soldier wore his military tunic (a tunic that was shorter than the standard civilian tunic) his soldiers' belt and his military boots. He also had a military cloak or...
No, at least not into battle. The toga was the hallmark of a Roman citizen, so some soldiers might have been able to wear it when they weren't in uniform (and only if they were upper-class). Togas...
The Romans wore red clothing for the same reasons that we do. Red is a bright, attractive, happy color. There was no particular significance in red clothing.