Were most swords roughly the length of the gladius, or are there examples of swords, say, the length of a medieval Longsword? Did the concept of a two-handed sword exist at that time, or was it restricted to the later periods of history?
Generally short, the roman Gladius was the staple sword of Romans throughout the empire's early history as well as during the republic. About 60-68cm in length, with some variant reaching the high seventies the Gladius' main focus was not on reach, but close combat working in tandem with the rest of the formation. This work especially well again formations with longer reaching weapons once the Roman could get in close, such as the Greek phalanxes in the battle of Cynoscephalae allowing for the conquest of Greece by Rome. As for long swords, these were not used in the early empire because Roman tactics relied heavily on a tight nit unit with an emphasis on the use of shields for defense from ranged weapons. If soldiers used two-handed swords then they wouldn't be able to have any defense against such things. However as the empire evolved we see a transition to longer reaching weapons. Quoted from a previous answer of mine:
Basically, the Roman army changed in a couple ways throughout those years such as through tactics, weapons and styles of fighting. First of all, with those thousand years come experience. From the Persians to the Goths, the Byzantines acquired knowledge of how to combat almost any kind of opponent they faced, as written down in Tactica by Emperor Leo VI (895–908). We know that by the time of Basil II, weapons of longer reach than the Gladius (short sword) were standard in the army to counter the longer reaches of some Barbarian weapons, the Kontarion Spear and Spathion Longsword were both adopted to make up for the short reach of the Gladius.
So basically while no, long swords were not used in the early roman empire, an evolution of weaponry can be observed as the empire evolves and adapts to new situations, eventually contributing to the longer reaches of weapons throughout Europe in the middle ages. Sources:
Byzantine and Modern Greek Studies, 31 (2007)
Dennis, George T. (1985), Three Byzantine Military Treatises, Washington DC
Dennis, George T. (1997), "The Byzantines in Battle", in Tsiknakis, K