Companions are not usable in Warzonse, the pvp instances of TOR. Teams of players from both factions fight against each other there, Republic versus Imperials. The Mods are classicle for Multiplayer games, like conquering control points and capture the flag variants. In the battles that have been shown it has been four vs. four, or eight vs. eight so far. Bioware also plans to do a warzone in which players of the same faction can compete, as to shorten queues.
In the open world there are going to be PVP-fights, and according to Zoeller even mission objectives: There will be special pvp objectives on the planets. It's possible that the factions will conquer buildings or take out enemy leaders. Zoeller: "With those objectives we're giving guidelines to the pvp and focus it on specific regions" On the question if there will be armed vehicles in battles, zoeller answered: "Maybe." That means, it could happen that players will fight each other with vehicles, if not on the open world then at least in Warzones.
Other then that there are going to be normal quests where you will compete against other players. Similar to Warhammer online there also will be quests that lead to contested areas, in which you will meet enemy players.
Sorry, just did a quick translation. If something is unclear or formulated stupid, please tell and I'll recheck it.