After. Arena takes place in May 2012, P4G's epilogue takes place in 2013.
Yes and no. The plot for most of the Investigation Team is basically rescuing another person (Labrys, though they were initially just investigating why the Midnight Channel turns back on and learn about her later) from the TV world and discovering whoever is behind it. The portions of the game surrounding Naoto, Labrys and the P3 cast are significantly different. Naoto's and the Ex-S.E.E.S. members revolve around finding what was stolen during a plane hijacking as well as who was behind it), and Elizabeth's is about understanding what it'll take to save the protagonist of Persona 3, culminating in receiving her own Fool Arcana card.
The antagonists (There's two) of Arena are a hacker that wants to use Labrys as the ultimate weapon and an unidentified supernatural entity using him a puppet.. Theories are floating around that it's Nyarlathotep (The Villain of Persona 2)
Arena is mostly linear. You can choose to an extent what characters you play as first, but the storylines themselves have only one path, save for a few dialogue options that determine whether or not you complete the route or get a joke ending.
And in all likelihood there's going to be at least 1 more sequel, as Arena ends with the Investigation Team planning to go to Tatsumi Port Island.